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

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Solution

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 prismStep 2: Formula usedBy prism formula,$\left(\delta \right)=i+e-A$Step 3: Solution Now, $i=e=\frac{3}{4}×60°=45°$Angle of deviation $\left(\delta \right)=i+e-A$$⇒\delta =45°+45°-60°\phantom{\rule{0ex}{0ex}}⇒\delta =30°$Hence, the angle of deviation is $30°$.

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