Question

The minimum deviation angle occurred by a prism of prism angle
60° is 60°. Calculate the refractive index of the material of prism.​

Answer 1

$\mathfrak{ \huge{ \red{ \underline{ \underline{ANSWER}}}}} \\ \\ \implies \sf \blue{ \bold{angle \: of \: prism \: (A) = \red{60 \degree}}} \\ \\ \implies \sf \blue{ \bold{minimum \: deviation \: (\delta \: m) = \red{60 \degree}}} \\ \\ \implies \sf \boxed{ \bold{ \pink{refractive \: index \: (\eta) = \orange{\frac{ \sin( \frac{A + \delta \: m}{2} ) }{ \sin( \frac{A}{2} )} } }}} \\ \\ \implies \sf \eta = \frac{ \sin( \frac{60 \degree + 60 \degree}{2} ) }{ \sin( \frac{60 \degree}{2} ) } = \frac{ \sin60 \degree}{ \sin30 \degree} = \sqrt{3 } \\ \\ \implies \sf \huge{\blue{ \underline{ \pink{\boxed{ \bold{ \orange{ \eta = \sqrt{3} }}}}}}}$

Answer 2

$\sf\huge{ \pink{ \underline{ \underline{Answer}}}} \\ \\ \longrightarrow \sf \: A = 60 \degree \\ \\ \longrightarrow \sf \delta \: m = 60 \degree \\ \\ \sf \implies\boxed{ \red{ \eta = \frac{ \sin( \frac{A + \delta \: m}{2} ) }{ \sin( \frac{A}{2} ) } }} \\ \\ \longrightarrow \sf \eta = \frac{ \sin( \frac{60 + 60}{2} ) }{ \sin( \frac{60}{2} ) } = \frac{ \sin(60) }{ \sin(30) } = \sqrt{3} \\ \\ \implies \sf \boxed{ \orange{ \bold{ \eta = \sqrt{3}}}}$