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 θ = 30°. The interfaces of the glass layers are parallel to each other. The refractive indices of the different glass layers decrease monotonically as nₘ = n - mΔn, where nₘ is the refractive index of the mth slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m - 1)th and mth slabs from the right side of the stack. What is the value of m?

Question

G1 Physics · Accepted Answer

Because all interfaces are parallel, n sinθ is conserved across the stack. Initially n sin30° = 1.6 × 1/2 = 0.8. At the slab from which the ray emerges parallel to the interface, the refracted angle is 90°, so nₘ = 0.8. Using nₘ = 1.6 - 0.1m gives 0.8 = 1.6 - 0.1m, hence m = 8. Therefore option A is correct.