A monochromatic light is travelling in a medium of refractive index...

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 $\theta = 30 ° .$ The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as ${n}_{m} = n – m\Deltan$ where ${n}_{m} is the refractive index of the$ {m}^{th} $slab and$ \Deltan = 0.1 $(see the figure). The ray is refracted out parallel to the interface between the$ {\left(m – 1\right)}^{th} and ${m}^{th}$ slabs from the right side of the stack. What is the value of m?
$A monochromatic light is travelling in a medium of refractive index n = 1.6 . It enters a stack of glass layers from$

Correct answer

Step-by-step solution

Applying snell's law between entry & exit surfaces,

$nsin θ = μ\sin \left(\dfrac{π}{2}\right)$

$\to 1.6sin {30}^{o} = μ\sin \left(\dfrac{π}{2}\right)$

$&there4; μ = 0.8$

$&there4; 0.8 = n - mΔn$

$= 1.6 - m × 0.1$

$&there4; m = 8$

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