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प्रश्न
State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air.
The refractive indices of glass and water with respect to vacuum are 3/2 and 4/3 respectively. If the speed of light in glass is 2 × 108m/s, find the speed of light in (i) vacuum, (ii) water.
उत्तर
The law of refraction that defines the refractive index of a medium with respect to the other is given by first law of refraction known as Snell’s law.
First law of refraction
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
This is known as Snell’s law. Mathematically, it can be given as follows:
`sini/sinr="constant"=` \[^aμ_b\]
Here, \[^aμ_b\] is the relative refractive index of medium b with respect to medium a. Consider a ray of light travelling from medium B into medium A. Let v1 be the speed of light in medium A and v2 be the speed of light in medium B. Then the refractive index of medium A with respect to medium B is given by
`n_(AB)=v_2/v_1`
If one medium is vacuum or air then the constant is named as absolute refractive index of the medium.
Let, absolute refractive index of glass, `n_g=3/2`
Absoluterefractive index of water, `n_w=4/3`
Speed of light in glass, vg = 2 × 108 m/s
(i) Speed of light in vacuum
`n_g=c/v_g`
`c=n_gxxv_g=3/2xx2xx10^8=3xx10^8 `m/s
(ii) Speed of light in water,
`n_w=c/v_w`
`v_w=c/n_w=(3xx10^8)/((4/3))=2.25xx10^8` m/s
संबंधित प्रश्न
The refractive index of diamond is 2.42. What is the meaning of this statement?
A ray of light travelling in water falls at right angles to the boundary of a parallel-sided glass block. The ray of light:
(a) is refracted towards the normal
(b) is refracted away from the normal
(c) does not get refracted
(d) is reflected along the same path
Fill in the following blank with a suitable word:
When a ray of light goes from air into a clear material, you see the ray bend. How much the ray bends is determined by the ............... of the material.
Define Snell's law of refraction. A ray of light is incident on a glass slab at an angle of incidence of 60°. If the angle of refraction be 32.7°, calculate the refractive index of glass. (Given : sin 60° = 0.866, and sin 32.7° = 0.540).
Light travels through air at 300 million ms−1. On entering water it slows down to 225 million ms−1. Calculate the refractive index of water.
Refractive indices of water, sulphuric acid, glass and carbon disulphide are 1.33, 1.43, 1.53 and 1.63 respectively. the light travels slowest in:
(a) sulphuric acid
(b) glass
(c) water
(d) carbon disulphide
The refractive index of glass with respect to air is `3/2` and the refractive index of water with respect to air is `4/3`. The refractive index of glass with respect to water will be:
(a) 1.525
(b) 1.225
(c) 1.425
(d) 1.125
A light ray enters from medium A to medium B as shown in figure. The refractive index of medium B relative to A will be ______.
How is the refractive index of material related to the velocity of light?
Absolute refractive indices of glass and water are `3/2 and 4/3` respectively. If the speed of light in glass is 2 × 108 m/s, the speed of light in water is ______.
