A ray of light incident on the horizontal surface of a glass slab at an angle of incidence I, just grazes the adjacent vertical surface after reflection. Compute the critical angle and refractive index of glass.

A ray of light incident on the horizontal surface of a glass slab at a

1.	A ray of light incident on the horizontal surface of a glass slab at an angle of incidence I, just grazes the adjacent vertical surface after reflection. Compute the critical angle and refractive index of glass.
Answer» Solution :By snell.s LAW of refraction, at the HORIZONTAL surface `1 times sin i=mu sin r, mu sin r= sin i`……….(1) Apply snell.s law at vertical surface, `mu sin c= 1 times sin 90^@, sin C=1/mu` From figure in `DELTA BFD` `r+C+90^@=180^@,c=90^@-r` `sin (90^@-r)=1/mu, mu cos r=1`.......(2) From equations 1 & 2 `mu^2 sin^2 r+mu^2+ cos^2 r=1+ sin^2 i` `mu=sqrt(1+ sin^2 i)` Critical angle is DETERMINED from `sin C=1/mu =1/sqrt(1+ sin^2 i)`