The refracting angle of a prism is A and the refractive index of the material of the prism is $cot \frac{A}{2}$ . The angle of minimum deviation of the prism is

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Answer 1

It is given $μ = c o t A / 2$

We know that:
$μ = \frac{s i n ( \frac{δ m + A}{2} )}{s i n A / 2}$

$\Rightarrow c o t A / 2 = \frac{s i n ( \frac{δ m + A}{2} )}{s i n ( A / 2 )}$

$\Rightarrow \frac{c o s A / 2}{s i n A / 2} = \frac{s i n ( \frac{δ m + A}{2} )}{s i n A / 2}$

$\Rightarrow s i n (π / 2 - A / 2) = s i n (\frac{δ m + A}{2})$

$\Rightarrow π / 2 - A / 2 = \frac{δ m + A}{2}$

$\Rightarrow π - 2 A = δ m$

Answer 2

It is given

μ = c o t A / 2

We know that:

μ = \frac{s i n ( \frac{δ m + A}{2} )}{s i n A / 2}

\Rightarrow c o t A / 2 = \frac{s i n ( \frac{δ m + A}{2} )}{s i n ( A / 2 )}

\Rightarrow \frac{c o s A / 2}{s i n A / 2} = \frac{s i n ( \frac{δ m + A}{2} )}{s i n A / 2}

\Rightarrow s i n (π / 2 - A / 2) = s i n (\frac{δ m + A}{2})

\Rightarrow π / 2 - A / 2 = \frac{δ m + A}{2}

\Rightarrow π - 2 A = δ m