JEE MAIN - Physics (2022 - 28th June Morning Shift - No. 12)
The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -
180 $$-$$ 2A
90 $$-$$ A
180 + 2A
180 $$-$$ 3A
Explanation
$$\mu = {{\sin \left( {{{{\delta _m} + A} \over 2}} \right)} \over {\sin (A/2)}} = \cot A/2$$
$$ \Rightarrow \cos A/2 = \sin \left( {{{{\delta _m} + A} \over 2}} \right)$$
$$ \Rightarrow {\pi \over 2} - {A \over 2} = {{{\delta _m} + A} \over 2}$$
$$ \Rightarrow \pi - 2A = {\delta _m}$$
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