Question

A ray of light falls normally on one face of the prism of relative index $\sqrt 2 $ and comes out at grazing emergence from the second surface. The angle of prism is
A.${30^ \circ }$
B.${60^ \circ }$
C.${45^ \circ }$
D.${0^ \circ }$

Answer 1

Hint:
To solve this we have to find out the angle of the prism. For finding the angle of the prism we have to calculate the angle of deviation and by applying Snell’s law we can find. And after substituting all the values we can calculate the angle of the prism.

Complete step by step solution:
A ray of light falls normally on the force of prism of the red\refractive index $\sqrt 2 $ and comes out at grazing emergence from the second surface.
So, first we have to calculate the angle of deviation. The angle of deviation can be defined as the angle between the angle of incident and the angle of reflection of a ray from one medium to another medium. This is known as angle of deviation.
Angle of deviation
$\Rightarrow \delta = i + i - \left( {r + {r^1}} \right)$
$\Rightarrow {r^1} = \theta $
That is, $i = {90^ \circ } = r$
Now, by applying Snell’s law we have to calculate.
$\Rightarrow {\mu _1}\sin i = {\mu _2}\sin r$
$\Rightarrow {r_1}\sin c = {\mu _2}\sin {i^1}$
Now putting the value of $\mu $
$\Rightarrow \sqrt 2 \sin c = 1\sin {90^ \circ }$
We know that,
$\Rightarrow \sin c = {1}{{\sqrt 2 }}$
Now, we have I and r
$\Rightarrow i = {90^ \circ }$ $r = {90^ \circ }$
Now, we have to calculate angle of prism for angle of prism we have to find $\delta $
$\Rightarrow \delta = i + i - \left( {r - {r^1}} \right)$
Now put the values.
$\Rightarrow 90 + 90 - \left( {45 + 90} \right)$
$\Rightarrow 90 + 90 - 135$
$\Rightarrow \delta = {45^ \circ }$
After substituting the value, we calculate angle of prism which is ${45^ \circ }$
So, this way the option (C) is correct.

Note:
For solving this question the step we have to keep in mind is to first find out the angle of deviation we will find $\theta $ after calculating this by applying Snell’s law we can find the angle of prism by substituting the value. These are some important points which we have to remember while solving this and in this way, we can find out the accurate answer.