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:

(a) What is the product of the ratio $\dfrac{\text {sin i}}{\text {sin r}}$ at the first surface and at the second surface?

(b) State whether the opposite surfaces are parallel or not parallel.

(c) How did you reach the conclusion in (b) above?

(a) At the first surface, from air to glass:

$\dfrac{\text {sin i}$1}{\text {sin r}1} = \text μ

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

At the second surface, from glass to air:

$\dfrac{\text {sin i}$2}{\text {sin r}2} = \dfrac{1}{\text μ} .

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

$\dfrac{\text {sin i}$1}{\text {sin r}1}\times \dfrac{\text {sin i}2}{\text {sin r}2} = \text μ \times \dfrac{1}{\text μ} = 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 be equal to the angle of incidence at the second surface and since these angles are not equal, the surfaces cannot be parallel.