An isosceles glass prime ( refractive index `=(3)/(2)`) has its base just submerged in water ( refractive index `= (4)/(3)`) . The base of the prism is horizontal. A horizontal light ray AB is incident on the prism and takes a path shown in figure to emerge out of the prism. Find the maximum value of base angle `theta` of the prism for which total internal reflection can take place at the base.

Answer

`theta_(max) = cos^(-1) (sqrt((17)/(21)))`