A light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to :

Step-by-step solution

At point A by Snell's law = 45^ r r= 1 2 At point B , for total internal reflection, i₁= 1 From figure, i₁=90^ -r aligned & ( 90^ -r )= 1 & r= 1 aligned Now r= 1- ^2 r = 1- 1 2 ^2 = 2 ^2-1 2 ^2 From eqs (ii) and (iii) 1 = 2 ^2-1 2 ^2 Squaring both sides and then solving, we get = 3 2