(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium with speed of light in vacuum. (b) The refractive indices of water and glass with respect to air are 4/3 and 3/2 respectively. If the speed of light in glass is 2�10^8ms ?1 , find the speed of light in (i) air, (ii) water.

Answer:

(a) Refractive index is defined as the ratio of the speed of light in a vacuum to its speed in a specific medium.

When a beam of light passes through two different media via an interface, its behaviour is governed by the laws of refraction of light. These laws are also known as Snell’s law. The two laws followed by a beam of light traversing through two media are:

(1) The ray of light incident to the interface, the normal trajectory of the beam (from the point of incidence), and the refracted ray must all lie in the same plane.

n = c/ν

where

n = Refractive index.

c = Velocity of light in a vacuum ( 3 × 108 m/s).

v = Velocity of light in a substance.

(2) For any two different media, the since of the angle at which the beam of light is incident is always proportional to the sine of the angle at which the refracted ray emerges. In other words, the quotient of the sine of the angle of incidence and the sine of the angle of refraction is always constant.

\(n = \frac{sin i}{sin r}\).

(b)

(i) nglass = c/νmedium

⇒ 3/2 = c/(2 × 108)

⇒ c = 3 × 108 m/s

(ii) nwater = c/νwater

νwater = (3 × 108)/(4/3)

νwater = (9/4)× 108 m/s

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