What should be the value of angle `theta` so that light entering normally through the surface AC of a prism `(n=3//2)` does not cross the second refracting surface AB?

Explanation

Light ray will pass the surface `AC` without bending since it is incident normally. Suppose it strikes the surface `AB` at an angle of incidence `i`.
`I = 90-theta`
For the required condition:
`90^(@) - theta gt C`
or `sin (90^(@) - theta) gt sin C`
or `cos theta gt sin c (1)/(3//2) = (2)/(3)` or `theta lt cos^(-1) (2)/(3)`