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Q.

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=300. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as  nm=n−mΔn, where nm  is the refractive index of mth the  slab and Δn=0.1 (see the figure). The ray is refracted out parallel to the interface between the  m−1th and mth  slabs from the right side of the stack. What is the value of m?

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answer is 8.

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Detailed Solution

nsin300=n−mΔnsin900​⇒1.612=1.6−m0.11​⇒m=8"m=8" ( but n for a material i.e n−mΔn can’t be less than “1” ).
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