Question

the refractive index of a material of equilateral prism is root 3, then angle of

minimum deviation of the prism is​

Answer 1

Given ,

• Refractive index of equilateral prism is √3
• Angle of equilateral prism is 60°

We know that ,

Refractive index of prism in terms of angle of minimum deviation and angle of prism is given by

$\mathtt{\fbox{refractive \: index \: of \: prism = \frac{ \sin( \frac{a + δm}{2} ) }{ \sin( \frac{a}{2} ) }}}$

Thus ,

$\sf \mapsto \sqrt{3} = \frac{ \sin( \frac{60 +δm }{2} ) }{ \sin( \frac{60}{2} ) }\\ \\ \sf \mapsto \sqrt{3} =\frac{ \sin( \frac{60 +δm }{2} ) }{ \sin( 30) } \\ \\ \sf \mapsto \frac{ \sqrt{3} }{2} = \sin( \frac{60 +δm }{2} ) \\ \\\sf \mapsto \sin(60) = \sin( \frac{60 +δm }{2} )$

On comparing LHS with RHS , we get

$\sf \mapsto 60 = \frac{60 \: + \: δm }{2} \\ \\ \sf \mapsto 120 = 60 + δm \\ \\\sf \mapsto δm = 60°$

Hence , the angle of deviation is 60°