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…

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?

Aicharya · Accepted Answer

Applying snell's law between entry & exit surfaces,

$n \sin θ = μ \sin (\frac{π}{2})$

$\Rightarrow 1.6 \sin 30^{o} = μ \sin (\frac{π}{2})$

$∴ μ = 0.8$

$∴ 0.8 = n - m Δ n$

$= 1.6 - m \times 0.1$

$∴ m = 8$

A monochromatic light is travelling in a medium of refractive index n = 1.6 . It enters a stack of glass…

Solution