Question 390: Ray Optics

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 $$	heta  = {30^ \circ }.$$ The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $${n_m} = n - m\Delta n,$$ where $${n_m}$$ is the refractive index of the $${m^{th}}$$ slab and  $$\Delta n = 0.1$$ (see the figure). The ray is refracted out parallel to the interface between the $${\left( {m - 1} ight)^{th}}$$ and $${m^{th}}$$ slabs from the right side of the stack. What is the value of $$m$$?

Accepted Answer

Applying Snell's law, we have nsin$$	heta$$ = (n $$-$$ m$$\Delta$$n)sin90$$^\circ$$ it is given that n = 1.6, $$	heta$$ = 30$$^\circ$$, $$\Delta$$n = 0.1. The above equation becomes
1.6sin30 = [1.6 $$-$$ m(0.1)]sin90
1.6 $$	imes$$ $${1 \over 2}$$ = (1.6 $$-$$ 0.1m) $$	imes$$ 1
0.8 = (1.6 $$-$$ 0.1m)
0.1m = 1.6 $$-$$ 0.8
0.1m = 0.8
m = 8

Ray Optics

Integer / Numeric Answer Type