Refraction - Introduction
Refraction is the change in direction of a wave due to a change in its medium.
It is essentially a surface phenomenon. The phenomenon is mainly in governance to the
law of conservation of energy and momentum. Due to change of medium, the phase
velocity of the wave is changed but its frequency remains constant. This is most
commonly observed when a wave passes from one medium to another at any angle
other than 90° or 0°. Refraction of light is the most commonly observed phenomenon,
but any type of wave can refract when it interacts with a medium, for example when
sound waves pass from one medium into another or when water waves move into water
of a different depth.
The following are the laws of refraction of light.
(i) The incident ray, the refracted ray and the normal to the
interface of two transparent media at the point of incidence, all
lie in the same plane.
(ii) The ratio of sine of angle of incidence to the sine of angle of
refraction is a constant, for the light of a given colour and for
the given pair of media. This law is also known as Snell’s law of
refraction.
If i is the angle of incidence and r is the angle of refraction, then,
sin i / sin r = constant
This constant value is called the refractive index of the second medium
with respect to the first. Let us study about refractive index in some detail.
Refractive Index
The extent of the change in direction that takes place in a given pair of media is expressed
in terms of the refractive index. The refractive index can be linked to an important physical
quantity, the relative speed of propagation of light in different media. It turns out that light
propagates with different speeds in different media. Light travels the fastest in vacuum with
the highest speed of 3×108 m s–1. In air, the speed of light is only marginally less,
compared to that in vacuum. It reduces considerably in glass or water. The value of the
refractive index for a given pair of media depends upon the speed of light in the two media.
Consider a ray of light travelling from medium 1 into medium 2. Let V1 be the speed of light
in medium 1 and V2 be the speed of light in medium 2. The refractive index of medium 2
with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the
speed of light in medium 2. This is usually represented by the symbol N21. This can be
expressed in an equation form as
N21 = (Speed of light in medium 1) / (Speed of light in medium 2) = (V1) / (V2)
By the same argument, the refractive index of medium 1 with respect to medium 2 is
represented as N12. It is given by
N12 = (Speed of light in medium 2) / (Speed of light in medium 1) = V1 / V2
Absolute Refractive Index
If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with
respect to vacuum. This is called the absolute refractive index of the medium. It is simply
represented as N2. If c is the speed of light in air and v is the speed of light in the
medium, then, the refractive index of the medium Nm is given by :
Nm = (Speed of light in air) / (Speed of light in the medium) = c / v
The absolute refractive index of a medium is simply called its refractive index.
Optical Density & Refractive Index
The ability of a medium to refract light is also expressed in terms of its optical density.
Optical density has a definite connotation. It is not the same as mass density.
We have been using the terms ‘rarer medium’ and ‘denser medium’ in this Chapter.
It actually means ‘optically rarer medium’ and ‘optically denser medium’, respectively.
When can we say that a medium is optically denser than the other?
In comparing two media, the one with the larger refractive index is optically denser
medium than the other. The other medium of lower refractive index is optically rarer.
The speed of light is higher in a rarer medium than a denser medium.
Thus, a ray of light travelling from a rarer medium to a denser medium slows down and
bends towards the normal. When it travels from a denser medium to a rarer medium,
it speeds up and bends away from the normal.
Refraction by Spherical Lenses
forms a lens. This means that a lens is bound by at least one spherical surface. In such
lenses, the other surface would be plane. A lens may have two spherical surfaces, bulging
outwards. Such a lens is called a double convex lens. It is simply called a convex lens. It
is thicker at the middle as compared to the edges. Convex lens converges light rays.
Hence convex lenses are called converging lenses. Similarly, a double concave lens is
bounded by two spherical surfaces, curved inwards. It is thicker at the edges than at the
middle. Such lenses diverge light rays. Such lenses are called diverging lenses. A double
concave lens is simply called a concave lens.
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| Concave Lens |
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| Concave Lens |
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| Convex Lens |
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| Convex Lens |
Image Formation in Lenses Using Ray Diagrams
(i) A ray of light from the object, parallel to the principal axis, after refraction from a
convex lens, passes through the principal focus on the other side of the lens. In
case of a concave lens, the ray appears to diverge from the principal focus located
on the same side of the lens.
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| Convex Lens |
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| Concave Lens |
(ii) A ray of light passing through a principal focus, after
refraction from a convex lens,will emerge parallel to the
principal axis. A ray of light appearing to meet at the
principal focus of a concave lens, after refraction, will emerge parallel to the principal
axis.
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| Convex Lens |
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| Concave Lens |
(iii) A ray of light passing through the optical centre of a lens will emerge without
any deviation.
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| Convex Lens |
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| Concave Lens |
The Lens Formula
This formula gives the relationship between object distance (u), image-distance (v)
and the focal length (f ).
(1/v) - (1/u) = (1/f)
The lens formula given above is general and is valid in all situations
for any spherical lens.
Magnification
The magnification produced by a lens is defined as the ratio of the height of the
image and the height of the object. It is represented by the letter m. If h is the
height of the object and h′ is the height of the image given by a lens, then the
magnification produced by the lens is given by,
m = (Height of the Image) / (Height of the object) = h'/h
Magnification produced by a lens is also related to the object-distance u, and
the image-distance v. This relationship is given by
Magnification (m ) = h′/h = v/u
Power of a Lens
The degree of convergence or divergence of light rays achieved by a lens is
expressed in terms of its power. The power of a lens is defined as the reciprocal
of its focal length. It is represented by the letter P. The power P of a lens of focal
length f is given by
P = 1/f
The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D. If f is
expressed in metres, then, power is expressed in dioptres. Thus, 1 dioptre
is the power of a lens whose focal length is 1 metre. 1D = 1 m^(–1).
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