Answer to Question #81924 in Optics for Becky

Question

Calculate the angle of minimum deviation of a prism if its
refracting angle is 60o
. The refractive index of the material of the
prism is 1.632

Answer 1

If δ is the angle of minimum deviation of light and A is the angle of the prism, then the refractive index of the prism will be

n=sin⁡((A+δ)/2)/sin⁡〖A/2〗 .

We have

n∙sin⁡〖A/2〗=sin⁡((A+δ)/2) → (A+δ)/2=arcsin⁡(n∙sin⁡〖A/2〗 ) → δ=2 arcsin⁡(n∙sin⁡〖A/2〗 )-A=

=2 〖∙arcsin〗⁡(1.632∙sin⁡〖(60°)/2〗 )-60°=49.36°.