Refraction of Light Class 10 Notes
Behaviour of light at the interface of two media
When light travelling in one medium (ray AO in figure) falls on the surface of a second medium, the following three effects may occur :
(i) A part of the incident light is turned back into the first medium (ray OB in figure). This is called reflection of light.
(ii) A part of the incident light is transmitted into the second medium along a changed direction (ray OC in figure). This is called refraction of light.
(iii) The remaining third part of light is absorbed by the second medium. This is called absorption of light.
Figure
Refraction of light
Concept of refraction of light
When light travels in the same homogeneous medium, it travels along a straight path. However, when it passes from one transparent medium to another, the direction of its path changes at the interface of the two media. This is called Refraction of light.
The phenomenon of the change in the path of the light as it passes from one transparent medium to another is called Refraction of light. The path along which the light travels in the first medium is called incident ray and that in the second medium is called Refracted ray. The angles which the incident ray and the refracted ray make with the normal at the surface of separation are called angle of incidence (i) and angle of refraction (r) respectively.
Laws of Refraction
Refraction of light follows the following two laws :
(i) The incident ray, the refracted ray and the normal to the surface separating the two media, all lie in the same plane.
(ii) The ratio of the sine of the incident angle (\angle i) to the sine of the refracted angle (\angle r) is constant for a pair of two media.
i.e. \frac{{\sin \,i}}{{\sin \,r}} = constant ………(1)
This constant is known as the refractive index 006Ff the medium in which refracted ray travels with respect to the medium in which incident ray travels. You will study refractive index later on in this chapter.
Refractive index of medium is denoted by ‘μ’
Thus equation 6.1 can be written as
\mu = \frac{{\sin \,i}}{{\sin \,r}} ………(2)
This law is also known as Snell’s law as it was stated by Prof. Willebrord Snell (Dutch mathematician and astronomer).
Cause of Refraction
We come across many media like air, glass, water etc. Every transparent medium has a property known as optical density. The optical density of a transparent medium is closely related to the speed of light in the medium. Optical density of a medium is the quantity which tells us whether a light wave will travel slower or faster in that medium or speed of a wave in any medium will depend on the optical density of that material. If the optical density of a transparent medium is low then the speed of light in that medium is high. Such a medium is known as optically rarer medium. Thus, optically rarer medium is that medium through which light travels fast. In other words, a medium in which speed of light is more is known as optically rarer medium.
On the other hand, if the optical density of a transparent medium is high then the speed of light in that medium is low. Such a medium is known as optically denser medium. Thus, optically denser medium is that medium through which light travels slow. In other words, a medium in which speed of light is less is known as optically denser medium.
Speed of light in air is more than the speed of light in water, so air is optically rarer medium as compared to the water. In other words, water is optically denser medium as compared to air. Similarly, speed of light in water is more than the speed of light in glass, so water is optically rarer medium as compared to the glass. In other words, glass is optically denser medium as compared to water.
When light goes from air (optically rarer medium) to glass (optically denser medium) such that the light in air makes an angle with the normal to the interface separating air and glass, then it bends from its original direction of propagation. Similarly, if light goes from glass to air, again it bends from its original direction of propagation. The phenomenon of bending of light from its path when it goes from one optical medium to another optical medium is known as refraction. We have seen that the speed of light in different media is different, so we can say that refraction of light takes place because the speed of light is different in different media.
Figure
It is observed that :
(i) When a ray of light passes from an optically rarer medium to a denser medium, it bends towards the normal (\angle r < \angle i), as shown in figure (A).
(ii) When a ray of light passes from an optically denser to a rarer medium, it bends away from the normal (\angle r > \angle i) as shown in figure (B).
(iii) A ray of light travelling along the normal passes undeflected, as shown in figure (C). Here \angle i = \angle r = 0º.
(iv) The intensity of the refracted ray is less than that of the incident ray. It is because there is partial reflection and absorption of light at the interface.
Refractive index
Refractive index in terms of speed of light
The refractive index of a medium may be defined in terms of the speed of light as follows :
The refractive index of a medium for a light of given wavelength may be defined as the ratio of the speed of light in vacuum to its speed in that medium.
Refractive index = \frac{{{\mathbf{Speed}}\,{\mathbf{of}}\,{\mathbf{light}}\,{\mathbf{in}}\,{\mathbf{vacuum}}}}{{{\mathbf{Speed}}\,{\mathbf{of}}\,{\mathbf{light}}\,{\mathbf{in}}\,{\mathbf{medium}}}}
or \mu = \frac{c}{v} ……….(3)
Refractive index of a medium with respect to vacuum is also called absolute refractive index.
Refractive index in terms of wavelength
Since the frequency (f) remains unchanged when light passes from one medium to another, therefore
\mu = \frac{c}{v} = \frac{{{\lambda _{vac}}\, \times \,f}}{{{\lambda _{med}}\, \times \,f}}
\mu = \frac{{{\lambda _{vac}}}}{{{\lambda _{med}}\,}} ……….(4)
So the refractive index of a medium may be defined as the ratio of wavelength of light in vacuum to its wavelength in that medium.
Relative refractive index
The relative refractive index of medium 2 with respect to medium 1 is defined as the ratio of speed of light (v1) in the medium 1 to the speed of light (v2) in medium 2 and is denoted by 1\mu 2.
Thus 1\mu 2 = \frac{{{{\text{v}}_{\text{1}}}}}{{{{\text{v}}_{\text{2}}}}} ……….(5)
As refractive index is the ratio of two similar physical quantities, so it has no units and dimensions.
Factors on which the refractive index of a medium depends
These are as follows :
(i) Nature of the medium.
(ii) Wavelength of the light used.
(iii) Temperature
(iv) Nature of the surrounding medium
It may be noted that refractive index depends on the wavelength of light but is independent of the angle of incidence.
Important Information
We know that speed greater than speed of light is not possible
So c > v [v = Velocity of light in given medium]
[c = Velocity of light in vacuum]
Now as μ = \frac{c}{v}, it should be greater than one.
When light travels from one medium to another medium, the velocity of light and its wavelength (\lambda ) changes but frequency (f) of light remains the same.
Since c = f λ and v = f {\lambda _m} [λm = wavelength of light in given medium]
∴ μ = \frac{c}{v} = \frac{\lambda }{{{\lambda _m}}}
Thus, refractive index of a medium of material depends upon the wavelength of the light falling on it. Refractive index of a medium is minimum for red light and maximum for violet light.
So wavelength of light in medium,
{\lambda _m} = \frac{\lambda }{\mu } = \frac{{{\mathbf{wavelength}}\,\,{\mathbf{of}}\,{\mathbf{light}}\,\,{\mathbf{in}}\,\,{\mathbf{air}}}}{{{\mathbf{refractive}}\,\,{\mathbf{index}}\,\,{\mathbf{of}}\,\,{\mathbf{medium}}}}As μ > 1 , so {\lambda _m} < \lambda . Thus, wavelength of light decreases when it travels from rarer medium like air to denser medium like water, glass etc.
When a ray of light falls normally on a medium, \angle i = 0 and hence \angle r = 0. Then refraction of light does not take place.
Snell’s law is not valid for the above case
Optically denser (or simply denser) medium is one whose refractive index is large as compared to other medium.
Optically rarer (or simply rarer) medium is one whose refractive index is small as compared to other medium.
Physical significance of refractive index
The refractive index of a medium gives the following two information’s :
(i) The value of refractive index gives information about the direction of bending of refracted ray. It tells whether the ray will bend towards or away from the normal.
(ii) The refractive index of a medium is related to the speed of light. It is the ratio of the speed of light in vacuum to that in the given medium. For example, refractive index of glass is 3/2. This indicates that the ratio of the speed of light in glass to that in vacuum is 2 : 3 or the speed of light in glass is two-third of its speed in vacuum.
Exercise
- Refractive index in term of speed of light is written as :
(A) \mu = \frac{{\text{c}}}{{\text{V}}}
(B) \mu = c·V
(C) \mu = \frac{{\text{V}}}{{\text{c}}}
(D) None of these
Answer- Refractive index depends on :
(A) Nature of medium
(B) Wavelength of light
(C) Temperature of medium
(D) All of these
Answer- Refractive index has unit :
(A) meter per second
(B) metre
(C) second
(D) unitless
Answer- Relative Refractive Index of medium 2 w.r.t. medium 1 is :
(A) 1\mu 2 = \frac{{{{\text{v}}_{\text{1}}}}}{{{{\text{v}}_{\text{2}}}}}
(B) 1\mu 2 = \frac{{{{\text{v}}_{\text{2}}}}}{{{{\text{v}}_{\text{1}}}}}
(C) 1\mu 2 = \frac{{\text{C}}}{{\text{v}}}
(D) None of these
Answer- The refractive index of kerosene is 1.42. Speed of light in it is :
(A) 4,26,000 km/s
(B) 300, 000 km/s
(C) 211,268 km/s
(D) 279,988 km/s
AnswerPrinciple of Reversibility of Light
“If the path of a ray of light is reversed after suffering a number of reflections and refractions, then it retraces its path” This is known as principle of reversibility of light.
Figure
A ray of light (AB) travelling in air (medium 1) strikes the surface of water (medium 2) at B and bends towards the normal NN’. The refracted ray BC strikes a plane mirror M normally as shown in figure.
Using Snell’s law, \frac{{{\rm{sin}}\,i}}{{{\rm{sin}}\,r}} = {\,_{\rm{1}}}{{\rm{\mu }}_{\rm{2}}}\, …(1)
Since the ray BC falls normally on the mirror, so it retraces its path along CB as shown in figure. In this case light travels from water to air, so according to snell’s law
\frac{{\sin \,\,r}}{{\sin \,\,i}} = {\,_2}{\mu _1} …(2)From (1) and (2)
_1{\mu _2}\,\, \times \,{\,_2}{\mu _1} = \frac{{\sin \,\,i}}{{\sin \,\,r}}\, \times \,\frac{{\sin \,\,r}}{{\sin \,\,i}} = 1or _1{\mu _2} = \frac{1}{{_2{\mu _1}}} …(3)
Thus, refractive index of medium 2 (water) with respect to medium 1 (air) is equal to the reciprocal of the refractive index of medium 1 (air) with respect to medium 2 (water).
Refraction through Glass slab
Description
Consider a rectangular glass slab, as shown in figure. A ray AB is incident on the face PQ at an angle of incidence i1. On entering the glass slab, it bends towards normal and travels along BC at an angle of refraction r1. The refracted ray BC is incident on face SR at an angle of incidence i2. The emergent ray CD bends away from the normal at an angle of refraction r2.
Figure : Refraction through glass slab
Using Snell’s law for refraction at face PQ,
\frac{{\sin \,{i_1}}}{{\sin \,{r_1}}} = _a{\mu _g} … (4)For refraction at face SR,
\frac{{\sin \,{i_2}}}{{\sin \,{r_2}}} =_g{\mu _a} = \frac{1}{{_{_a{\mu _g}}}} … (5)
Multiplying (7.4) and (7.5), we get
\frac{{\sin \,{i_1}}}{{\sin \,{r_1}}} × \frac{{\sin \,{i_2}}}{{\sin \,{r_2}}} = 1 (6)Now from figure we can say that ∠r1 = ∠i2 [
r1 and i2 are alternate opposite angles]
So equation can be written as
\frac{{\sin \,{i_1}}}{{\sin \,{r_1}}} ×\frac{{\sin \,{i_2}}}{{\sin \,{r_2}}} = 1⇒ sin i1 = sin r2
⇒ i1 = r2
Thus the emergent ray CD is parallel to the incident ray AB, but it has been laterally (sidewise) displaced with respect to the incident ray. This shift in the path of light on emerging from a refracting medium with parallel faces is called lateral displacement.
Hence lateral shift is the perpendicular distance between the incident and emergent rays, when light is incident obliquely on a refracting slab with parallel faces.
Factors on which lateral shift depends
(i) Lateral shift varies directly with the thickness of glass slab.
(ii) Lateral shift varies directly with the incident angle.
(iii) Lateral shift varies directly with the refractive index of glass slab.
Compound Slab
A compound slab is made of two or more media (say water and glass) bounded by parallel faces and is placed in air. A compound slab can be made by placing a glass tray completely filled with water on a glass slab.
When an incident ray AB travelling in air (medium 1) strikes the water surface (medium 2) at B and since water is denser than air so it will bend towards normal in water so it is refracted along BC. ∠ABN = i, incident angle and \angle N'BC = r1, angle of refraction.
Figure : Refractions through a compound slab
Now the ray BC acts as an incident ray for the surface separating glass slab and water and as glass is denser than water So refracted ray CD will bend towards normal in glass so the incident ray BC after striking this surface at C is refracted along CD in glass (medium 3). \angle \,{\bf{BC}}{{\bf{N}}_1} = r1, angle of refraction will acts as angle of incidence for water glass interface.
The ray CD acts as an incident ray for the surface separating glass slab and air. So the incident ray CD after striking this surface at D is refracted along DE in air that is it will bend away from normal. The rays DE and AB are parallel, so \angle \,{{\bf{N}}_{\bf{2}}}{\bf{'}}\,{\bf{DE}}= ∠ABN = i. In this case, \angle \,{\bf{CD}}{{\bf{N}}_2}= r2, incident angle and \angle \,{{\bf{N}}_{\bf{2}}}{\bf{'}}\,{\bf{DE}} = i, angle of refraction.
In this case also the incident and emergent rays are parallel it can be easily proved as we have proved in the case of glass slab.
Real and apparent depth
It is on account of refraction of light that the apparent depth of an object placed in denser medium is less than the real depth when viewed from rarer medium. Figure, shows a point object O placed at the bottom of a beaker filled with water. The rays OA and OB starting from O are refracted along AD and BC, respectively. These rays appear to diverge from point I.
So, I is the virtual image of O. Clearly, the apparent depth AI is smaller than the real depth AO. That is why a water tank appears shallower or an object placed at the bottom appears to be raised.
From Snell’s law, we have
Figure : (a) real and apparent depths Figure : (b)
2μ1 =\frac{{\sin \,i}}{{\sin \,r}} = \frac{{\sin \,\angle {\bf{AOB}}}}{{\sin \,\angle {\bf{AIB}}}} =\frac{{{\bf{AB}}\,{\bf{/}}\,{\bf{BO}}}}{{{\bf{AB}}\,{\bf{/}}\,{\bf{BI}}}} = \frac{{{\bf{BI}}}}{{{\bf{BO}}}} [see figure (b)]
As the size of the pupil is small, the ray BC will enter the eye only if point B is close to point A. Then
BI 
AI and BO AO.
1μ2 = \frac{1}{{_2{\mu _1}}} = \frac{{{\bf{AO}}}}{{{\bf{AI}}}} … (7)
or refractive index = \frac{{{\bf{real}}\,{\bf{depth}}}}{{{\bf{apparent}}\,{\bf{depth}}}}
or apparent depth = \frac{{{\bf{real}}\,{\bf{depth}}}}{{{\bf{refractive}}\,{\bf{index}}}} … (8)
As the refractive index of any medium (other than vacuum) is greater than unity, so the apparent depth is less than the real depth when viewed from rarer medium.
Important : On the other hand if the object is placed in a rarer medium and it is viewed from denser medium then apparent depth is greater than real depth.
Normal shift
The height through which an object appears to be raised in a denser medium is called normal shift. In figure we can see that
Normal shift = Real depth – Apparent depth
or d = AO – AI = AO – \frac{{{\rm{AO}}}}{{_{\rm{1}}{{\rm{\mu }}_{\rm{2}}}}} [ from (7) AI = \frac{{{\rm{AO}}}}{{_{\rm{1}}{{\rm{\mu }}_{\rm{2}}}}}]
= AO \left( {1 - \frac{1}{{_1{\mu _2}}}} \right) or d = t \left( {1 - \frac{1}{{_1{\mu _2}}}} \right) ... (9)
Clearly, the normal shift in the position of an object placed in a denser medium when seen through a rarer medium depends on two factors :
(i) the real depth of the object or the thickness (t) of the refracting medium
(ii) the refractive index of the denser medium. The higher the value of , greater is the normal shift ‘d’.
Effects of refraction of light
The refraction of light leads to some optical illusions. These are :
(i) A pencil or a stick immersed in water appears bent and short in length
(ii) A water tank appears shallow i.e., less deep than its actual depth,
(iii) An ink dot on a paper appears to be raised up when a glass slab is placed over it.
(iv) A fisherman fails to catch a fish if he aims the spear at the head of the fish.
(v) Apparent flattening of the sun at sunrise and at sunset.
Now we shall discuss all these effects in detail.
A pencil appears bent and short in water
Consider a pencil PQ. Let AQ portion of the pencil be dipped in water as shown in figure 7.5. Rays of light from the tip (Q) of the pencil bend away from the normal as they go from water to air i.e. denser to rarer medium. These rays appear to come from a point B. Thus, the dipped portion of the pencil appears as AB. Hence a pencil appears bent and short when immersed in water.
Figure
A water tank appears shallow i.e. less deep than its actual depth
Consider an object O say a stone lying on the bed of a water tank as shown in figure. A ray (OB) of light from the object suffers refraction at the free surface of water in the tank and bends away from the normal along BC. The refracted ray BC appears to come from point I which is above the object O. Thus, the bed of the tank appears at the level of point I. In other words, water tank appears shallow.
Figure
An ink dot on a paper appears to be raised up when a glass
slab is placed over it
The rays of light from the ink dot bend away from the normal as they go from the glass slab to air. The refracted rays AC and BD appear to come from point I. The point I is the virtual image of the ink dot and its position is above the ink dot O. Hence, an ink dot on a paper appears to be raised up when a glass slab is placed over it, as shown in figure.
Figure
A fisherman fails to catch a fish if he aims the spear at the head of fish.
Figure
This is also due to refraction of light. When a fish in water is seen from some angle, then due to refraction of light, the fish appears to be raised up and moreover the image of the fish is a little ahead of the actual position of the fish (see figure). As a result of this, the spear falls ahead of the actual position of the head of the fish. Thus, the fisherman is unable to catch the fish. However, a skilled fisherman always aims at the tail of the fish to catch the fish.
Apparent flattening of the sun at sunrise and sunset
The sun near the horizon appears flattened. This is due to atmospheric refraction. The density and the refractive index of atmosphere decreases with altitude, so the rays from the top and bottom portions of the sun on the horizon are refracted by different degrees. This cause the apparent flattening of the sun. But the rays from the sides of the sun on a horizontal plane are generally refracted by the same amount, so the sun still appears circular along its sides.
Apparent shift in the position of the sun at sunrise and sunset
Due to the atmospheric refraction, the sun is visible before actual sunrise and after actual sunset.
Figure : Refraction effect at sunset and sunrise
With altitude, the density and hence refractive index of air-layers decreases. The light rays starting from the sun S travel from rarer to denser layers. They bend more and more towards the normal.
However, an observer sees an object in the direction of the rays reaching his eyes. So to an observer standing on the earth, the sun which is actually in a position below the horizon, appears in the position S’, above the horizon. The apparent shift in the position of the sun is by about 0.50. Thus the sun appears to rise early by about 2 minutes and for the same reason, it appears to set late by about 2 minutes. This increases the length of the day by about 4 minutes.
Tyndall effect
The earth’s atmosphere is a heterogeneous mixture of minute particles. These particles include smoke, tiny water droplets, suspended particles of dust and molecules of air. When a beam of light strikes such fine particles, the path of the beam becomes visible. The light reaches us, after being reflected diffusely by these particles. The phenomenon of scattering of light by the colloidal particles gives rise to Tyndall effect.
This phenomenon is seen when a fine beam of sunlight enters a smoke filled room through a small hole. Thus, scattering of light makes the particles visible. Tyndall effect can also be observed when sunlight passes through a canopy of a dense forest. Here, tiny water droplets in the mist scatter light.
The colour of the scattered light depends on the size of the scattering particles. Very fine particles scatter mainly blue light while particles of larger size scatter light of longer wavelengths. If the size of the scattering particles is large enough, then, the scattered light may even appear white.
Colour of the sun at sunrise and sunset
Light from the sun near the horizon passes through thicker layers of air and travels relatively larger distance in the earth’s atmosphere before reaching our eyes. However, light from the sun overhead would travel relatively shorter distance (see figure) . At noon the sun appears white as only a little of the blue and violet colours are scattered. Near the horizon, most of the blue light and shorter wavelengths are scattered away by the particles. Therefore, the light that reaches our eyes is of longer wavelengths. This gives rise to the reddish appearance of the sun.
Figure
Total Internal Reflection
Description
The phenomenon when a ray of light travelling from a denser to rarer medium is sent back to the same denser medium provided it strikes the interface of the denser and the rarer media at an angle greater than the critical angle is called total internal reflection.
When a ray of light falls on the interface separating denser and rarer medium at B. It is refracted along BB’. As the angle of incidence increases, the refracted ray bends towards the interface. At a particular angle of incidence, the refracted light travels along the interface and the angle of refraction is 90°(i.e. r = 90°). The angle of incidence for which angle of refraction becomes 90° is called critical angle (C).
Figure
When the angle of incidence becomes greater than the critical angle, there is no refracted light and all the light is reflected back in the denser medium. This phenomenon is known as total internal reflection.
Conditions for Total Internal Reflection
(i) The light should travel from denser to rarer medium.
(ii) The angle of incidence must be greater than the critical angle for the given pair of media.
Relation between refractive index of the medium and the critical angle
When a ray of light goes from denser medium (2) to the rarer medium (1), then according to Snell’s Law.
2µ1 = \frac{{\sin i}}{{\sin r}}
When angle of incidence i = C (the critical angle) then angle of refraction r = 90°
2µ1 = \frac{{\sin {\rm{C}}}}{{\sin {\rm{ }}90^\circ }} = sin C
2µ1 = \frac{1}{{_1{\mu _2}}}
∴ 1µ2 = \frac{1}{{\sin {\rm{C}}}} .......(1)
or sin C = \frac{1}{{_1{\mu _2}}}
Important Note
During total internal reflection of light, the whole incident light energy is reflected back to the parent optically denser medium.
(i) Critical angle of a medium depends upon the wavelength of light.
since µ ∞ \frac{1}{{{\lambda ^2}}} , so sin C ∞ λ2.
Greater the wavelength, greater will be the critical angle. Thus, critical angle of a medium will be maximum for red colour and minimum for violet colour.
(ii) Since µ =\frac{{\rm{C}}}{{\rm{V}}} = \frac{{f\lambda }}{{f{\lambda _m}}} = \frac{\lambda }{{{\lambda _m}}} , λm= wavelength on light in medium and λ = wavelength of light in vacuum/air
sin C = \frac{{{\lambda _m}}}{\lambda } ......(2)
(iii) Critical angle depends upon the nature of the pair of media. Greater the refractive index, lesser will be the critical angle.
sin C = \frac{1}{\mu }
(iv) Images formed due to TIR are much brighter because total light is reflected back into the same medium and there is no loss of intensity of light.
Problem : What is the value of refractive index of a medium, if the critical angle is 45° ?
Solution : µ = \frac{1}{{\sin {\rm{C}}}} = \frac{1}{{\sin {\rm{4}}5^\circ }} = \sqrt 2
Some phenomena due to total internal reflection
(i) Working of Porro Prism
A right angled isosceles prism is called Porro-Prism. It can be used in Periscopes or Binocular.
The critical angle for glass is equal to 41.8°. When the ray of light falls on the face of a right angled prism at angle greater than 41.8°, it will suffer total internal reflection.
Right angled prisms used to bend the light through 90° and 180° are shown in figures (a) & (b) respectively. A right angled prism used to invert the image of an object without changing its size in shown in figure.
(a) (b) (c)
Figure : Working of porro prism
Additional Information
Mirrors can also be used for bending the rays of light. But the intensity of the beam reflected by mirrors is low because even a highly polished mirror does not reflect the whole light. On the other hand, in porro-prism the whole light is reflected. Therefore, there is no loss of intensity of light and hence image is bright.
(ii) Sparking or brilliance of a diamond
The refractive index of diamond is 2.5 which gives, the critical angle as 24°. The faces of the diamond are cut in such a way that whenever light falls on any of the faces, the angle of incidence is greater than the critical angle i.e. 24°. So when light falls on the diamond, it suffers repeated total internal reflections. The light which finally emerges out from few places in certain directions makes the diamond sparkling.
(iii) Shining of air bubble in water
The critical angle for water-air interface is 48° 45'. When light propagating in water (denser medium) is incident on the surface of air bubble (rarer medium) at an angle greater than 48° 45', the total internal reflection takes place. Hence the air bubble in water shines brilliantly (See figure).
Figure
(iv) Mirage
Mirage is an optical illusion of water observed generally in deserts when the inverted image of an object (e.g. a tree) is observed alongwith the object itself on a hot day.
Figure : Mirage formation in deserts
Due to the heating of the surface of earth on a hot day, the density and hence the refractive index of the layers of air close to the surface of earth becomes less. The temperature of the atmosphere decreases with height from the surface of earth so the value of density and hence the refractive index of the layers of air at higher altitude is more. The rays of light from distant objects (say a tree) reaches the surface of earth with an angle of incidence greater than the critical angle. Hence the incident light suffers total internal reflections as shown in the figure. When an observer sees the object as well as the image he gets the impression of water pool near the object
(a) The mirage formed in hot regions is called inferior mirage.
(b) Superior mirage is formed in cold regions. This type of mirage is called looming.
(v) Optic pipe and optical fibres
Optical fibre is extremely thin (radius of few microns) and long strand of very fine quality glass or quartz coated with a thin layer of material of refractive index less than the refractive index of the strand. (If refractive index of the strand is say 1.7 then refractive index of the coating is 1.5) The coating or surrounding of optical strands is known as cladding and the optical strand is known as core. The sleeve containing a bundle of optical fibres is called a light pipe.
When light falls at one end of the optical fibre, it gets refracted into the fibre. The refracted ray of light falls on the interface separating core and cladding at an angle which is greater than the critical angle. The total internal reflection takes place again and again as shown in figure. The light travels the entire length of the fibre and arrives at the other end of the fibre without any loss in its intensity even if the fibre is rounded or curved.
Figure : Working of an optical fibre
Uses
(a) Optical fibres are used to transmit light without any loss in its intensity over distances of several kilometer.
(b) Optical fibre are used in the manufacture of medical instrument called endoscopes. Light pipe is inserted into the stomach of the human being. Light is sent through few optical fibres of the light pipe. The reflected light from the stomach is taken back through the remaining optical fibres of the same light pipe. This helps the doctors to see deeply into the human body. Hence the doctor can visually examine the stomach and intestines etc. of a patient.
(c) They are used in tele-communication for transmitting signals. A single fibre is able to transmit multiple signals (say 3000) simultaneously without interference, whereas the electric wire can preferably transmit one signal at a time.
(d) Optical fibres are used to transmit the images of the objects.
(e) Optical fibres are used to transmit electrical signals from one place to another. The electrical signals are converted into light by special devices called transducers. Then these light signals are transmitted through optical fibres to distant places.
Spherical Lenses
Definition
A lens is a piece of transparent refracting material bound by two spherical surfaces or one spherical and other plane surface.
A lens is the most important optical component used in microscopes, telescopes, cameras, projectors, etc.
Basically lenses are of two types :
(i) Convex lens or converging lens (ii) Concave lens or diverging lens
Convex lens and their types
A lens which is thick at the centre and thin at the edges is called a convex lens. The most common form of a convex lens has both the surfaces bulging out at the middle. Some forms of convex lenses are shown in the figure.
(a) (b) (c)
Figure
Concave lens and their types
A lens which is thin at the middle and thick at the edges is called a concave lens. The most common form of a concave lens has both the surfaces depressed inward at the middle. Some forms of concave lenses are shown in the figure.
(a) (b) (c)
Figure : Different types of concave lens
Definitions in connection with spherical lenses
(i) Centre of curvature (C)
The centre of curvature of the surface of a lens is the centre of the sphere of which it forms a part. Because a lens has two surfaces, so it has two centres of curvature. Points C1 and C2 of figure (a) and shows centre of curvatures.
Figure : Characteristics of convex and concave lenses
(ii) Radius of curvature (R)
The radius of curvature of the surface of a lens is the radius of the sphere of which the surface forms a part. R1 and R2 in figure (a) and (b) are the radius of curvatures of two spheres.
(iii) Principal axis (C1C2)
It is the line passing through the two centres of curvature of the lens.
(iv) Optical centre
If a ray of light is incident on a lens such that after refraction through the lens the emergent ray is parallel to the incident ray, then the point at which the refracted ray intersects the principal axis is called the optical centre of the lens. In the figure (a) and (b) O is the optical centre of the lens. It divides the thickness of the lens in the ratio of the radii of curvature of its two surfaces. Thus :
\frac{{{\rm{O}}{{\rm{P}}_1}}}{{{\rm{O}}{{\rm{P}}_2}}} = \frac{{{{\rm{P}}_1}{{\rm{C}}_1}}}{{{{\rm{P}}_2}{{\rm{C}}_2}}} = \frac{{{{\rm{R}}_1}}}{{{{\rm{R}}_2}}}If the radii of curvature of the two surfaces are equal, then the optical centre coincides with the geometric centre of the lens.
Figure
For the ray passing through the optical centre, the incident and emergent rays are parallel. However, the emergent ray suffers some lateral displacement relative to the incident ray. The lateral displacement decreases with the decrease in thickness of the lens. Hence a ray passing through the optical centre of a thin lens does not suffer any lateral deviation, as shown in the figure (b) and (c).
(v) Principal foci and focal length
First principal focus
It is a fixed point on the principal axis such that rays starting from this point (in convex lens) or appearing to go towards this point (concave lens), after refraction through the lens, become parallel to the principal axis. It is represented by F1 or F'. The plane passing through this point and perpendicular to the principal axis is called the first focal plane. The distance between first principal focus and the optical centre is called the first focal length. It is denoted by f1 or f'. (See figure)
Figure
Second principal focus
It is fixed point on the principal axis such that the light rays coming parallel to the principal axis, after refraction through the lens, either converge to this point (in convex lens) or appear to diverge from this point (in concave lens). The plane passing though this point and perpendicular to principal axis is called the second focal plane. The distance between the second principal focus and the optical centre is called the second focal length. It is denoted by f2 or f.
Figure
Generally, the focal length of a lens refers to its second focal length. It is obvious from the above figures that the foci of a convex lens are real and those of a concave lens are virtual. Thus the focal length of a convex lens is taken positive and the focal length of a concave lens is taken negative.
If the medium on both sides of a lens is same, then the numerical values of the first and second focal lengths are equal. Thus
f = f ′
(vi) Aperture
It is the diameter of the circular boundary of the lens. In figure, (a) & (b), AB is the aperature of lens.
Figure
Rules for image formation by A convex lens
The position of the image formed by a convex lens can be found by considering two of the following rays
(i) A ray of light coming parallel to principal axis, after refraction through the lens, passes through the principal focus (F) as shown in the figure.
Figure
(ii) A ray of light passing through the optical centre O of the lens goes straight without suffering any deviation as shown in the figure.
Figure
(iii) A ray of light coming from the object and passing through the principal focus of the lens after refraction through the lens, becomes parallel to the principal axis. This is shown in figure.
Figure
Image formed by convex lens :
The position, size and nature of the image formed by a convex lens depends upon the distance of the object from the optical centre of the lens. For a thin convex lens, the various cases of image formation are explained below :
(i) When object lies at infinity
When an object lies at infinity, the rays of light coming from the object may be regarded as a parallel beam of light. The ray of light BO passing through the optical centre O goes straight without any deviation. Another parallel ray AE coming from the object, after refraction, goes along EA'. Both the reflected rays meet at A' in the focal plane of the lens. Hence, a real, inverted and highly diminished image is formed on the other side of the lens in its focal plane. (See figure)
Figure
(ii) When object lies beyond 2F
When an object lies beyond 2F, its real, inverted and diminished image is formed between F and 2F on the other side of the lens as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal focus F and goes along EF. Another ray AO passing through the optical centre O goes straight without suffering any deviation. Both the refracted rays meet at A′. Hence a real, inverted and diminished image is formed between F and 2F on the other side of the convex lens. (See figure)
Figure
(iii) When object lies at 2F
When an object lies at 2F in front of a convex lens, its real inverted image having same size as that of the object is formed on the other side of the convex lens as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal focus F and goes along EF. Another ray AO passing through the optical centre O goes straight without suffering any deviation. Both the refracted rays meet at A Hence a real, inverted image having the same size as that of the object is formed at 2F on the other side of the lens. (See figure)
Figure
(iv) When object lies between F and 2F
When an objects lies between F and 2F in front of a convex lens, its real, inverted and magnified image is formed beyond 2F on the other side of the lens as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal focus F and goes along EF. Another ray of light AO passing through the optical centre goes straight without any deviation. Both these refracted rays meet at A'. Hence a real, inverted and magnified image is formed beyond 2F on the other hand side of the lens. (See figure)
Figure
(v) When object lies at F
When an object lies at the principal focus F of a convex lens, then its real, inverted and highly magnified image is formed at infinity on the other side of the lens as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal focus F and goes along EF. Another ray of light AO passing through the optical centre O goes straight without any deviation. Both these refracted rays are parallel to each other and meet at infinity. Hence a real, inverted, highly magnified image is formed at infinity on the other side of the lens. (See figure)
Figure
(vi) When object lies between O and F
When an object lies between the optical centre O and the principal focus F of a convex lens, then its virtual, erect and magnified image is formed on the same side as that of the object as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, passes through the principal focus F and goes along EF. Another ray of light AO passing through the optical centre goes straight without any deviation. Both these refracted rays appear to meet at A', when produced backwards. Hence a virtual, erect and enlarged image is obtained on the same side as the object. (See figure)
Figure
The results of image formation by a convex lens are summarised in the Table
Table
Rules for image formation by A concave lens
The position of the image formed by a concave lens can be found by considering following two rays coming from a point object (as explained below).
(i) A ray of light coming parallel to the principal axis, after refraction, appears to pass through the principal focus F of the lens, when produced backwards (See figure(a)).
(ii) A ray of light passing through the optical centre O of the lens goes straight without suffering any deviation (See figure (b)).
Figure
Image formed by concave lens :
The image formed by a concave lens is always virtual, erect and diminshed and is formed between the optical centre O and the principal focus F of the lens. For a thin concave lens of small aperature, the cases of image formation are discussed below :
(i) When the object lies at infinity
When object lies at infinity in front of a concave lens, a virtual, erect, highly diminished image is formed at the principal focus F as explained below. The rays of light AE and BD coming parallel to the principal axis of the concave lens, after refraction, go along EG and DH respectively. When extended in the backward direction, these refracted rays appears to be coming from the principal focus F. Hence a virtual, erect and highly diminished image is formed at the principal focus F. (See figure)
Figure
(ii) When object lies between O and ∞
When an object lies at any position between the optical centre O and infinity in front of a concave lens, the image formed is virtual erect and diminished and is formed between the optical centre O and the principal focus F as explained below :
A ray of light AE coming parallel to the principal axis, after refraction, goes along EG and appears to pass through the principal focus F when produced backwards, another ray of light AO passing through optical center O goes straight without any deviation. Both these refracted rays appear to meet at A'. Hence, a virtual, erect and diminished image is formed between O and F. (See figure)
Figure
The summary of image formation by a concave lens for different positions of the object is given in Table.
Table
New Cartesian Sign Convention
(i) All distances are measured from the optical centre of the lens.
(ii) The distances measured in the same direction as the incident light are taken as positive.
(iii) The distances measured in the direction opposite to the direction of the incident light are taken as negative.
(iv) Heights measured upwards and perpendicular to the principal axis are taken as positive.
(v) Heights measured downwards and perpendicular to the principal axis are taken as negative.
Figure shows the above given points.
Figure
Consequences of the sign convention :
(i) The focal length (f) of a converging (convex) lens is positive and that of a diverging (concave) lens is negative.
(ii) Object distance (u) is always negative.
(iii) The distance of real image (v) is positive and that of virtual image is negative.
(iv) The object height h1 is always positive. Height h2 of virtual erect image is positive and that of real inverted image is negative.
(v) The linear magnification m = h2/h1 is positive for a virtual image and negative for a real image.
Lens Formula
(i) Object distance (u)
Distance of object from the optical centre of a lens is known as object distance. It is denoted by u.
(ii) Image distance (v)
Distance of image from the optical centre of a lens is known as image distance. It is denoted by v.
(iii) The relation between object distance (u), image distance (v) and focal length (f) of a lens is called lens formula. The lens formula is given by
– \frac{1}{u} + \frac{1}{v} = \frac{1}{f}
or \frac{{{\rm{-1}}}}{{{\rm{distance}}\,\,{\rm{of}}\,\,{\rm{object}}\,\,{\rm{from}}\,\,{\rm{lens}}}} + \frac{{\rm{1}}}{{{\rm{distance}}\,\,{\rm{of}}\,\,{\rm{image}}\,\,{\rm{from}}\,\,{\rm{lens}}}} = \frac{{\rm{1}}}{{{\rm{focal}}\,\,{\rm{length}}\,{\rm{of}}\,{\rm{lens}}}}
Derivation :
Consider a convex lens of focal length f. Let an object (AB) be placed normally on the principal axis of the lens. A real image A'B' of this object is formed by the convex lens on the other side as shown in the figure.
Figure
Triangle ABO and A'B'O are similar
∴ \frac{{AB}}{{A'B'}} = \frac{{OA}}{{OA'}} … (1)
Also, triangles OFC and A'B'F are similar
∴ \frac{{OC}}{{A'B'}} = \frac{{OF}}{{FA'}} … (2)
But OC = AB∴ \frac{{AB}}{{A'B'}} = \frac{{OF}}{{FA'}} = \frac{{OA}}{{OA'}} … (3)
Since all distances are measured from the optical centre (O) of the lens, so FA' = OA' – OF
Hence eqn. (3) becomes \frac{{OA}}{{OA'}} = \frac{{OF}}{{OA' - OF}} … (4)
Using sign conventions, OA = – u
distance measured opposite to the direction of incident light)
OA' = +v (distance in the direction of incident light)
OF = +f (distance in the direction of incident light)
Substituting these values in eqn (10.4), we get
\frac{{ - u}}{v} = \frac{f}{{v - f}}or –uv + uf = vf
Dividing both sides by uvf, we get
\frac{{ - uv}}{{uvf}} +\frac{{uf}}{{uvf}} = \frac{{vf}}{{uvf}}– \frac{1}{f}+\frac{1}{v} = \frac{1}{u}
or –\frac{1}{u}+ \frac{1}{v} = \frac{1}{f}
which is lens formula
Magnification :
The size or height of image formed by a lens depends upon the position of the object from the optical centre of the lens. It means a lens can produce images of different sizes depending upon the position of a given object.
The ratio of the size (or height) of the image to the size (or height) of the object is known as the magnification (m) produced by the lens.
From the fig we can say that Magnification (m)
= \frac{{{\rm{size}}\,{\rm{(or}}\,{\rm{height)}}\,{\rm{of}}\,{\rm{image}}\,{\rm{(}}A{\rm{'}}B{\rm{')}}}}{{{\rm{size}}\,{\rm{(or}}\,{\rm{height)}}\,{\rm{of}}\,{\rm{object}}\,{\rm{(}}AB{\rm{)}}}}=\frac{{h'}}{h} … (5)
Figure
Magnification (m) in terms of u and v
In the figure AB is the size or height of the object and A'B' is the size or height of the image
Δ's AOB and A'OB' are similar
∴ \frac{{A'B'}}{{AB}} = \frac{{OA'}}{{OA}} … (6)
Applying sign conventions,
A'B' = –h; AB = h
OA' = + v, OA = –u
∴ eqn (10.6) becomes
\frac{{ - h'}}{h}= \frac{v}{{ - u}} or \frac{{h'}}{h} =\frac{v}{u} … (7)But, m = \frac{{h'}}{h}
Using eqn. (7), we get
m = \frac{{h'}}{h} = \frac{v}{u}
Thus, magnification of a lens = \frac{{{\rm{image}}\,{\rm{distance}}}}{{{\rm{object}}\,{\rm{ditance}}}}
(i) Magnification (m) is positive if the image produced by a lens is virtual.
(ii) Magnification in case of a concave lens is always positive as it always forms a virtual image.
(iii) Magnification in case of a convex lens is positive when it forms a virtual image but magnification in case of a convex lens is negative when it forms a real image.
Q. 1 A 2 cm long pin is placed perpandicular to the principal axis of a convex lens of focal langth 12 cm. The distance of a pin from the lens is 15 cm. Find the size of the image.
Ans. V = 60 cm, M = –4, he = –8 cm
Q. 2 A 4 cm high object is placed at a distance of 60 cm from a concave lens of focal length 20 cm. Find the size of image.
Ans. he = 1 cm
Power :
Power of a lens is defined as the reciprocal of the focal length of the lens (expressed in meters). It is denoted by P.
i.e. P = \frac{1}{{f\,({\rm{in}}\,{\rm{m}})}} or P = \frac{{100}}{{f\,({\rm{in}}\,{\rm{cm}})}}
Thus, we can say that a lens of small focal length has large power of converging or diverging a parallel beam of light. On the other hand, a lens of large focal length has small power of converging or diverging a parallel beam of light. Since a convex lens converges a parallel beam of light, so it has a power of converging the beam. When a convex lens has a large power, it means, this convex lens strongly converges the parallel beam of light and near to its optical centre. On the other hand, when a convex lens has a small power, then this lens converges the parallel beam of light but away from its optical centre.
Unit of power of a lens is diopter (D).
Definition of diopter (D)
Power of a lens is 1 diopter if its focal length is 1 metre.
Power of convex lens is positive.
Power of concave lens is negative.
Combination of two lenses :
Consider two lenses of focal lengths f1 and f2 respectively. When these lens are in contact, the combination behaves as a single lens of focal length f. This focal length (f) is known as equivalent focal length and is given by \frac{1}{f} =\frac{1}{{{f_1}}} + \frac{1}{{{f_2}}}
Since \frac{1}{f} = P, power of lens, so the power of the combination of two lenses is given by
P = P1 + P2
Where, P =\frac{1}{f} , P1 = \frac{1}{{{f_1}}}and P2 = \frac{1}{{{f_2}}}
If number of lenses of powers P1, P2, P3,...............etc. are placed in contact with each other, then the power of this combination of lenses is given by
P = P1 + P2 + P3 + ……
Note :
(i) If a convex lens is placed in contact with a concave lens and a power of this combination is positive, then combination of these lenses behaves as a convex lens.
(ii) If a convex lens is placed in contact with a concave lens and the power of this combination is negative, the combination of these lenses behaves as a concave lens.
Refraction due to a prism
Prism :
A prism is a wedge shaped portion of a transparent refracting medium bounded by two plane faces inclined to each other at a certain angle. In the following figure.
The two plane faces (ABED and ACFD) inclined to each other are called refracting faces of the prism.
The line (AD) along which the two refracting faces meet is called the refracting edge of the prism.
The third face (BCFE) of the prism opposite to the refracting edge is called the base of the prism.
The angle A included between the two refracting faces is called angle of the prism.
Figure
Any section of the prism cut by a plane perpendicular to the refracting edge is called principal section of the prism.
Determination of angle of deviation :
Let abc be the principal section of a prism of refracting angle A. Let a light ray AB be incident on the refracting surface ab of the prism at an angle i. After refraction at B, the ray of light bends towards the normal NO and travels along BC. The refracted ray BC again suffers a refraction at C and bends away from the normal N'O and travels along CD. The ray CD is called emergent ray. The angle made by the emergent ray with the normal is called angle of emergence (i.e.∠e). When the emergent ray is produced backward, it meets the incident ray produced forward at point M. The angle between the emergent ray and the incident ray is called angle of deviation. (d).
Figure : Deviation of light through prism
Angle of deviation is the angle through which incident ray is turned by the prism while passing through it. In other words, the angle between the emergent ray and the direction of incident ray is called angle of deviation.
Determination of angle of deviation (d)
At surface ab of the prism, the incident ray AB is deviated along BC.
From Figure , ∠MBC = ∠MBO – ∠CBO
or 
1 = i – r1 … (8)
1 is the deviation produced by the ab surface of the prism.
Similarly, at surface ac, the ray BC is deviated along CD, so
2 = e – r2 … (9)
2 is the deviation produced by the ac surface of the prism
∴ Total angle of deviation, = 1 + 2
or = i – r1 + e – r2 = (i + e) – (r1 + r2) … (10)
From quadrilateral ABOC,
∠A + ∠ABO + ∠BOC + ∠OCA = 360°
But ∠ABO = ∠OCA = 90°
∴ ∠A + ∠ABO + ∠BOC + ∠OCA = 360°
or ∠A + ∠BOC = 180° … (11)
From ΔBOC, ∠r1 + ∠BOC + ∠r2 = 180° … (12)
From eqn. (10.11) and (10.12), we get
∠A + ∠BOC = ∠r1 + ∠BOC + ∠r2
or A = r1 + r2 … (13)
Subsituating the value of eqn. (10.13) in eqn. (10.10), we get
= i + e – A
or + A = i + e … (10.14)
Thus, sum of angle of deviation and the angle of prism is equal to the sum of the incident angle and the angle of emergence.
Note : If refractive index of the material of prism is less than the refractive index of the medium of its surrounding, the emergent ray may bend away from the base of the prism as shown in the figure.
Figure
Factors on which angle of deviation depends :
(i) The angle of incidence (ii) The material of the prism
(iii) The wavelength of light used (iv) The angle of the prism.
Dispersion of light
The phenomenon of splitting of white light (i.e., polychromatic light) into its constituent colours (say when it passes through a glass prism) is called dispersion of light.
When white light beam falls on a prism, the emergent light consists of different colours i.e. red, orange, yellow, green, blue, indigo, and violet which are the constituent colours of white light. The phenomenon is called dispersion of light. We generally observes only five colours in the spectrum because it is difficult to differentiate blue, indigo and violet (see figure).
Figure
Cause of dispersion :
The separation of different colours present in white light is because of different deviation faced by them when they pass through a prism (as speed of different colour is different in a medium).
The wavelength of different colours is different. Red colour has maximum wavelength and violet colour has minimum wavelength i.e., λr > λv. Therefore, \mu for red colour is less than that for the violet colour i.e., µr < µv
Now deviation produced by small angled prism is given by
= (µ – 1) A
∴ r = (µr – 1) A and v = (µv – 1) A
Hence, r < v
This shows that the red colour deviates least and the violet colour deviates the most. The other colours suffer deviation in between the red and the violet colours.
(i) In vacuum dispersion of light does not take place because all colours travel in vacuum with same speed.
(ii) In crown glass, velocity of red light is simply 1% more than that of violet light.
(iii) µr < µ0 < µy < µg < µb < µi < µv
Additional Information
Sound waves in air do not show dispersion.
Recombination of the spectrum
Figure
White light can be dispersed into the constituent colours by a prism. Newton showed that the reverse is also true, i.e., the seven colours of the spectrum can be recombined to obtain white light as explained below :
Suppose two glass prisms of the same material and of the same angle A are placed in such a way that the prism P2 is upside down w.r.t. the prism P1 as shown in the figure. The first glass prism P1 splits (disperses) the white light into seven colours. When these colours fall on the inverted prism P2, all the colours are refracted in the opposite direction by an equal amount and combine to give white light.
Thus, the first glass prism disperses (splits) white light into seven colours and the second glass prism placed upside down recombines these seven colours of the spectrum to produce white light.
Rainbow :
Rainbow is one of the most beautiful example of spectrum formed by the dispersion of sunlight by water droplets hanging in the atmosphere after light dazzling.
These small droplets of water acts like a dispersive medium. When sunlight falls on these droplets it suffers total internal reflection as well as dispersion. The constituent colours of sunlight are refracted by different amounts and band of seven colour is formed called rainbow.
Additional content
Laser beam consists of light of single colour (or single wave length) so when it is made incident on a glass prism it will not show dispersion.
Human Eye
The human eye is one of the most sensitive sense organ of sight which enables us to see the wonderful world of light and colour around us. It is like a camera having a lens system and forming an inverted, real image on a light sensitive screen inside the eye. The structure and working of the eye is as follows :
(i) Structure and working of human eye
The human eye is nearly spherical in shape having diameter about 2.3 cm with a slight bulge in the front part as shown in the figure. The transparent bulged portion is called cornea. Light enters the eye through cornea.
Figure : Structure of human eye
There is a (diaphragm of dark muscular assembly called iris) which controls the size of the pupil. The pupil can adjust its size according to the intensity of light and helps in regulating the amount of light entering into the eye. The size of pupil becomes smaller for bright light and larger for dim light. Behind the iris, there is a converging eyelens composed of fibrous, jelly-like material and is held in position by ciliary muscles. The curvature of the lens can be modified to some extent by these ciliary muscles. When the muscles are relaxed, the focal length of the lens is about 2.5 cm and we can see distant objects clearly. When we look at nearby objects, the ciliary muscles contract and the lens becomes more rounded and its focal length decreases.
The space between cornea and eyelens is filled with aqueous humor. The cornea and aqueous humor act as a lens and provide most of the refraction for light rays entering into the eye. The eyelens merely provides the fine adjustment of focal length required to focus objects at different distances. The light entering the eye is focussed by the eyelens which forms a real and inverted image of the object on the retina behind the lens. The retina is a delicate semi-transparent membrane having very large number of light-sensitive cells and is equivalent to the screen (photographic plate) of a camera. The retina has large number of rods and cones. The rods respond to the intensity of light and the cones respond to the colour of light. When light enters into the eye and falls on the retina, the light-sensitive cells get activated and generate electrical nerve pulses which are sent to the brain via the optic nerve. The brain processes these signals and we see the objects as they are. The most sensitive portion of retina is known as the yellow spot. It is slightly raised portion with a slight depression known as the Fovea centralis. The point where optic nerve enters the eye is totally insensitive to light and is called the blind spot.
(ii) Power of Accommodation
The images of the objects at different distances from the eye are brought to focus on the retina by changing the focal length of the eyelens which is composed of fibrous jelly-like material which can be modified to some extent by the ciliary muscles.
When we look at distant objects, the ciliary muscles are relaxed, eye lens is thin and focal length of the eyelens is about 2.5 cm. When we look at nearby object, the ciliary muscles contract so that the eyelens takes a more rounded shape and focal length of the eyelens decreases so as to focus light from the nearby objects on the retina. This ability or property of the eyelens to adjust its focal length so that it can see objects lying at all distances between the near point and the far point, is called accommodation.
A normal human eye can accommodate for all distances between infinity (far point) and about 25 cm (near point). The maximum variation of the power of the eyelens so as to focus the far (distant) objects and near objects on to the retina is called the power of accommodation of the eye. For a young adult, the power of accommodation of the eye (with normal vision) is about 4 dioptre.
(iii) Near Point and Far Point
The nearest point at which a small object can be seen distinctly by the eye is called the near point. For a normal eye, it is about 25 cm and is denoted by the symbol D.
With advancing age, the power of accommodation of the eye decreases as the eye lens gradually loses its flexibility. For most of the old persons aged nearly 60 years, the near point is about 200 cm and corrective glasses are needed to see the nearby objects clearly.
The farthest point upto which our eye can see objects clearly, without any strain on the eye is called the far point. For a person with normal vision, the far point is at infinity.
(iv) Least Distance of Distinct Vision
The minimum distance of an object from the eye at which it can be seen most clearly and distinctly without any strain on the eye, is called the least distance of distinct vision. For a person with normal vision, it is about 25 cm and is represented by the symbol D i.e.
Least distance of distinct vision (D) = 25 cm.
(v) Persistence of Vision
The image formed on the retina of the eye does not fade away instantaneously, when the object is removed from the sight. The impression (or sensation) of the object remains on the retina for about (1/16)th of a second, even after the object is removed from the sight. This continuance of the sensation of eye is called the persistence of vision.
Let a sequence of still pictures is taken by a movie camera. If the sequence of these still pictures is projected on a screen at a rate of 24 images or more per second then the successive impressions of the images on the screen appear to blend or merge smoothly into one another. This is because an image (or a scene) on the screen appears just before the impression of previous image on the retina is lost. Hence, the sequence of images blend into one another giving the impression of a moving picture. This principle is used in motion picture projection or in cinematography.
(vi) Colour-Blindness
The retina of our eye has large number of light sensitive cells having shapes of rods and cones. The rod-shaped cells respond to the intensity of light with different degrees of brightness and darkness whereas the cone shaped cells respond to colours. In dim light rods are sensitive, but cones are sensitive only in bright light. The cones are sensitive to red, green and blue colours of light to different extents.
Due to genetic disorder, some persons do not possess some cone-shaped cells that respond to certain specific colours only. Such persons cannot distinguish between certain colours but can see well otherwise. Such persons are said to have colour-blindness. Driving licenses are generally not issued to persons having colour-blindness.
(vii) Colour Perception of Animals
Different animals have different colour perception due to different structure of rods and cones. For example, bees have some cone-shaped cells that are sensitive to ultraviolet light. Therefore bees can see objects in ultraviolet light and can perceive colours which we cannot. Human beings cannot see in ultraviolet light as their retina do not have cone-shaped cells that are sensitive to ultraviolet light. The retina of chicks have mostly cones and only a few rods. As cones are sensitive to bright light only, therefore, chicks wake up with sunrise and sleep in their resting place by the sunset.
(viii) Cataract
Sometimes due to the formation of a membrane over the crystalline lens of some people in the old age, the eye lens becomes hazy or even opaque. This is called cataract. It results in decrease or loss in vision of the eye. Cataract can be corrected by surgery leading to normal vision.
Defects of vision and their correction
People with normal vision can focus clearly on very distant objects. We say their far point is at infinity. People with normal vision can also focus clearly on near objects upto a distance of 25 cm. We say their near point is at a distance of 25 cm from the eye.
(i) Shortsightedness (Myopia)
A person who can see the near objects clearly but cannot focus on distant objects is short sighted. The far point of a short-sighted person may
be only a few metres rather than at infinity. This defect occurs if a person’s eyeball is larger than the usual diameter. In such a case, the image of a distant object is formed in front of the retina as shown in the figure. It is because the eyelens remains too converging, forming the image of the object in front of the retina.
Figure : Image formation in Myopia
To correct short-sighted vision, a diverging lens (concave lens) of suitable focal length is placed in front of the eye. The rays of light from distant object are diverged by the concave lens so that final image is formed at the retina. You can think of the concave lens as performing a trick on the eye. If the object is very far off (i.e. u ∞ ) then focal length of the concave lens is so chosen that virtual image of the distant object is formed at the far point F of the short-sighted eye. Therefore rays of light appear to come from the image at the far point F of the short-sighted eye and not from the more distant object. (See figure).
Figure : Correction of image formation in myopia by using concave lens
Note that focal length of the lens for a short-sighted person is equal to the negative value of the person’s far point.
(ii) Farsightedness (Hyperopia or Hypermetropia)
A person who can see distant objects clearly but cannot focus on near by objects, is farsighted. Whereas the normal eye has a near point of about 25 cm, a farsighted person may have a near point several metres from the eye (see figure (b)). This defect may occur if the diameter of person’s eyeball is smaller than the usual or if the lens of the eye is unable to curve when ciliary muscles contract. In such a case, for an object placed at the normal near point (i.e. 25 cm from eye), the image of the object is formed behind the retina as shown in the figure (a). It is because the lens of the eye is not sufficiently converging to focus the object located at the normal near point.
A farsighted person has the normal far point but needs a converging lens in order to focus objects which are as close as 25 cm. The converging lens of correct focal length will cause the virtual image to be formed at the actual near point of the farsighted person's eye.
Figure : Correction of Hypermetropia by using convex lens
(iii) Presbyopia
This defect arises with aging. A person suffering from this defect can see neither nearby objects nor distant objects clearly/distinctly. This is because the power of accommodation of the eye decreases due to the gradual weakening of the ciliary muscles and diminishing flexibility of the eye lens.
This defect can be corrected by using bifocal lenses. Its lower part consists of a convex lens and is used for reading purposes whereas the upper part consists of a concave lens and is used for seeing distant objects.
(iv) Astigmatism
A person suffering from the defect cannot simultaneously focus on both horizontal and vertical lines of a wire gauze.
Figure
This defect arises due to the fact that the cornea is not perfectly spherical and has different curvatures for horizontally and vertically lying objects. Hence, objects in one direction are well focussed whereas objects in the perpendicular direction are not well focussed (see figure). This defect can be corrected by using cylindrical lenses. The cylindrical lenses are designed in such a way so as to compensate for the irregularities in the curvature of cornea (see figure).
Figure : Cylindrical lens