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 Δ$$n=0.1$$ (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?

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  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 Δ$$n=0.1$$ (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?

Infinity Learn · Accepted Answer

$$nsin300=n$$−mΔ$$nsin900$$​⇒$$1.612=1.6$$−$$m0.11$$​⇒$$m=8$$"$$m=8$$" $$($$ but n for a material i.e n−mΔn can’t be less than “$$1$$” $$)$$.

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