Consider the situation shown in figure. Find the maximum angle theta for which the light suffers total internal reflection at the vertical surface.

Explanation

The critical angle for this case is
`theta''=sin^-11/1.25=sin^-14/5`
or sintheta''=4/5`
since `theta''=pi/2-theta`, we have `sintheta'=costheta''=3/5`. From Snell's law,
`(sintheta)/(sintehta')=1.25`
`or, sintheta=1.25xxsintheta`
`=1.25xx3/5=3/4`
or `theta=sin^-13/4`
If `theta'' is greater than the critical angle `theta` will be smaller thasn this value. Thus the maximum value thet for which total reflection takes place at the vertical surface, is `sin^-1(3/4)`