A pair of perfectly parallel plane mirrors is separated by a distance
PHYSICS · Multi-part · CBSE · Physics · Light — Reflection and Refraction · Light — Reflection and Refraction
Problem
A pair of perfectly parallel plane mirrors is separated by a distance d. A narrow light ray enters the region between the mirrors making an angle θ with the normal to the left-hand mirror. The entry point lies a distance d/2 from the left mirror and is level with the midpoint of the mirror faces. The ray undergoes n reflections in total before eventually exiting at the far end.
Answer the following questions symbolically in terms of d, n, and θ.
(a) Show that the horizontal distance between successive reflection points on the same mirror is 2dtanθ. Explicitly state the geometric relationships you use.
(b) Derive an expression for the total horizontal displacement of the beam from entry to exit after n reflections.
(c) Using the results above, obtain a formula for the total path length L(n) of the beam between entry and exit.
(d) Evaluate L(n) numerically for d=1.5m, θ=25∘, and n=6. Express your answer to three significant figures.