Question

A monochromatic light is travelling in a medium of refractive index n = 1.6. It enters a stack of glass layers from the bottom side at an angle q = 30°. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as n_m= n – mΔn, where n_m is the refractive index of the m^th slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m – 1)^th and m^th slabs from the right side of the stack. What is the value of m?

Answer 1

(8) Here n × sin 30° = [n – m × 0.1] sin 90°
∴ 1.8 × sin 30° = 1.8 – m × 0.1 ∴ m = 8