Question

A ray of light passing through a prism having refracting index root 2 suffers minimum deviation it is found that angle of incidence is double the angle of refraction within prism find angle of prism

Answer 1

Explanation:

Given A ray of light passing through a prism having refracting index root 2 suffers minimum deviation it is found that angle of incidence is double the angle of refraction within prism find angle of prism

Let I be the angle of incidence and r be the angle of refraction.

We know that i = 2 x r

Now by Snell’s law we get

Sin i / sin r  

= sin 2 r / sin r

= 2 sin r cos r / sin r (sin 2 x = 2 sinx cos x)

= 2 cos r = √ 2

 So cos r = √2 / 2

               = 1 / √2

So r = 45 degree

Now minimum deviation A = r1 + r2  

                                              = 2 r  (since r1 = r2)

                                     So A = 2 x 45

                                        A = 90 degree.