Question

Horizontal rays of red light (λ = 660 nm, in vacuum) and violet light (λ = 410 nm, in vacuum) are incident on the flint-glass prism shown in the drawing. The indices of refraction for the red and violet light are n_red = 1.662 and n_violet = 1.698. The prism is surrounded by air. What is the angle of refraction for (a) red ray, (b)violet ray as it emerges from the prism?

Answer 1

The ray is incident normally on the glass. Therefore, it enters into the glass with out any deviation. It strikes the other surface. Since the top angle is 25 degree, the angle between the surface and the ray is now 65 degree.

If we draw a normal at the point of incidence, the angle of incidence inside the glass is now 25 degree.

We have to calculate the angle of refraction.

We know refractive index is ratio of sine of angle in vacuum or air (incident or refraction) /sine of angle in glass (refraction or incident).

Part - a

For red, refractive index is given as 1.662

Therefore, 1.662 = sin of angle in vacuum / sin 25,

Therefore, sin of angle in vacuum = 1.662 x sin 25 = 0.7024.

now

A = sin-1(0.7024) = 44.62

Similarly

Part - b

sind = 1.698 x sin (25)

which gives us

sind = 0.717606

or

A = sin-1 (0.717606)

which gives us the required angle, which is

a = 45.8572°