Question

A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each of these is equal to ${\frac{3}{4}}^{th}$ of the angle of the prism. The angle of deviation is

Answer 1

Step 1: Given

The angle of incidence $\left(i\right)=$ The angle of emergence $\left(e\right)=\frac{3}{4}A$

The prism is in equilateral shape, $A=60°$. Here, $A$ is the angle of the prism

Step 2: Formula used

By prism formula,

$\left(\delta \right)=i+e-A$

Step 3: Solution

Now, $i=e=\frac{3}{4}\times 60°=45°$

Angle of deviation $\left(\delta \right)=i+e-A$

$$\begin{gathered} \Rightarrow \delta =45°+45°-60° \\ \Rightarrow \delta =30° \end{gathered}$$

Hence, the angle of deviation is $30°$.