Question

A ray is incident perpendicularly on the surface AB of a transparent
glass slab.& is totally reflected at the surface CD. The minimum
refractive index of the material of the slab is-
A) 2/√3
B) √2
C) 2
D) 3/2​

Answer 1

Answer:

C) 2

Explanation:

1)  We a ray incident perpendicularly on the surface AB at I of a transparent glass slab.

Surrounding is air.

Let the refractive index of glass slab be 'n'.

Angle of incidence = 0 degree

r=Intial Angle of refraction

By Snell's Law,

$1*sin(0^{\circ})=n*sin(r)\\ \\=>r=0^{\circ}$

=> when incident ray incidents normally to the slab,then refracted ray follows it without any deviation.

2) Let the angle of incidence on  surface CD at R be $\theta$.

Sum of all angles of a quadrilateral ABIR is 360 degree.

$\angle A+\angle D+\angle I+\angle R=360^{\circ}\\ \\ =>75^{\circ}+75^{\circ}+90^{\circ}+90^{\circ}+\theta=360^{\circ}\\ \\=>\theta=30^{\circ}$

3) Since, ray is totally reflected at surface CD.

For minimum refractive index of slab, Refraction angle is 90 degree.

Using Snell's Law,

$n*sin(\theta)=1*sin(90^{\circ})\\ \\=>n*sin(30^{\circ})=1\\ \\=>n*\frac{1}{2} =1\\ \\=>n=2$

The minimum refractive index of slab is 2.