Question

A ray of light enters a glass block from air and comes out from the opposite surface. If the angle of refraction at the first surface is not the same as the angle of incidence at the second surface, then:

1. What is the product of the ratio `(sin i)/(sin r)` at the first surface and at the second surface?
2. State whether the opposite surfaces are parallel or not parallel?
3. How did you reach the conclusion (b) above?

Answer 1

a. At the first surface, from air to glass:

`(sin i_1)/(sin r_1)` = μ

Where μ is the refractive index of glass with respect to air.

At the second surface, from glass to air:

`(sin i_2)/(sin r_2) = 1/mu`

Therefore, the product of the two ratios is given by,

`(sin i_1)/(sin r_1) xx (sin i_2)/(sin r_2) = mu xx 1/mu`

= 1

Hence, the product of the ratio is 1.

b. The opposite surfaces are not parallel.

c. If the opposite surfaces were parallel, the angle of refraction at the first surface would equal the angle of incidence at the second surface. Since these angles are not equal, the surfaces cannot be parallel.