Question

a ray of light passes through a equilateral glass prism , such that the angle of incidence is equal to the angle of emergence . if the angle of emergece is 3/4 times the angle of prism , then the angle of deviation is ?

Answer 1

Answer:

$\boxed{\sf Angle \ of \ deviation\ (\delta ) = 60^\circ }$

Given:

Angle of incidence (i) = Angle of emergence (e)

Angle of emergence (e) = $\frac{3}{4}$ times Angle of prism (A)

To Find:

Angle of deviation ($\delta$)

Explanation:

As the prism is a equilateral glass prism, all the angles of the prism is equal to 60° each.

So,

Angle of prism (A) = 60°

According to the question;

$\sf i = e = \frac{3}{4} A$

Formula of angle of deviation of prism:

$\boxed{ \bold{ \delta = i + e - A}}$

i = e:

$\sf \implies \delta = e + e - A$

$\sf \implies \delta = 2e - A$

$\sf e = \frac{3}{4} A :$

$\sf \implies \delta = 2 \times \frac{3}{4} A - A$

$\sf \implies \delta = \frac{3}{2} A - A$

$\sf \implies \delta = \frac{3}{2} A - \frac{2}{2} A$

$\sf \implies \delta = \frac{3 - 2}{2} A$

$\sf \implies \delta = \frac{1}{2} A$

A = 60° :

$\sf \implies \delta = \frac{1}{2} \times 60 ^ \circ$

$\sf \implies \delta = 30 ^ \circ$

$\therefore$

Angle of deviation ($\delta$) = 30°