A ray of light passes through equilateral prism such that the angle of incidence is equal to angle of…
A ray of light passes through equilateral prism such that the angle of incidence is equal to angle of emergence and each of these angles is equal to $\left(\frac{3}{4}\right)^{\mathrm{th}}$ the angle of prism. The angle of deviation is
$35^{\circ}$
$40^{\circ}$
$20^{\circ}$
$30^{\circ}$
Solution
Let the angle of incidence of light at prism. $\mathrm{i}=\mathrm{x}$
So, Angle of emergence , $\mathrm{e}=\mathrm{x}$
Angle of prism, $A=\frac{4}{3} x$
Since prism is equilateral $\Rightarrow 3 \mathrm{~A}=180^{\circ} \Rightarrow \mathrm{x}=45^{\circ}$ From prism formula:
Angle of deviation, $\delta=\mathrm{i}+\mathrm{e}-\mathrm{A}=45+45-60=30^{\circ}$