A light ray in a parallel-sided slab

Problem statement

Question 3.B.- A light ray strikes a slab of thickness $e = 3$ cm from the air, with an angle of incidence of $48^\circ$. The refractive index of the slab is $n = 1.7$. After being refracted at the top face, the ray is reflected at the lower face of the slab and comes back out into the air, as shown in the figure. Determine:

a) (0.5 marks) The angle of refraction at the top face.

b) (1 mark) The time the refracted ray takes to reach the lower face of the slab.

c) (1 mark) The separation $x$ between rays (1) and (2).

Data: Speed of light in vacuum, $c = 3\cdot10^{8}\ \text{m s}^{-1}$; Refractive index of air, $n = 1$.

[Figure: horizontal parallel-sided slab, with air above and below and the thickness $e$ marked on the left. A ray arrives from the upper left at the top face; through the point of incidence passes the normal, vertical, drawn dash-dotted. From that point the reflected ray (1) leaves towards the upper right. The refracted ray goes down to the right to the lower face, is reflected there and rises to the top face, where ray (2) leaves into the air, parallel to (1). The distance $x$ is marked on the top face, between the point of incidence and the exit point of ray (2).]

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Physics · Question 3.B. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.