JEE Main 2025 Jan 23 Shift 2, Physics Q3: Prism

JEE Main2025Jan 23, Shift 2Physics

The refractive index of the material of a glass prism is $3$ . The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

A
$5 0^{\circ}$
B
$6 0^{\circ}$
C
$5 8^{\circ}$
D
$4 8^{\circ}$

Solution

Prism formula at minimum deviation: $μ = \frac{sin ( \frac{A + δ _{min}}{2} )}{sin ( \frac{A}{2} )}$ .

With $δ_{min} = A$ : $μ = \frac{sin A}{sin ( A /2 )} = \frac{2 sin ( A /2 ) cos ( A /2 )}{sin ( A /2 )} = 2 cos (A /2) .$

$3 = 2 cos (A /2) \Rightarrow cos (A /2) = \frac{3}{2} \Rightarrow A /2 = 3 0^{\circ} \Rightarrow A = 6 0^{\circ} .$

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JEE Main 2025 Jan 23 Shift 2, Physics Q3: Prism

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