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 paral

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 $θ = 30 ° .$ The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_{m} = n - m Δ n$ where $n_{m}$ is the refractive index of the $m^{t h}$ slab and $Δ n = 0.1$ (see the figure). The ray is refracted out parallel to the interface between the ${(m - 1)}^{t h}$ and $m^{t h}$ slabs from the right side of the stack. What is the value of m?

TestHub · Accepted Answer

Applying snell's law between entry & exit surfaces, n sin ⁡ θ = μ sin ⁡ π 2 ⇒ 1.6 sin ⁡ 30 o = μ sin ⁡ π 2 ∴ μ = 0.8 ∴ 0.8 = n - m Δ n = 1.6 - m × 0.1 ∴ m = 8

Physics - Geometrical Optics Question with Solution | TestHub

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