If the critical angle for the medium of a prism is C and this angle of prism is A, then there will be no emergent ray when

Let $r_1$ be the angle of refraction at first face and ${\mathrm{r}}_2$ be the angle of refraction at second face. as $r_1+r_2=A$

thus,$(r_1+r_2>2C)$

This is possible if $r_2>\mathrm{C}$ (as if $r_1>$ C incident ray would not enter the prism). ${\mathrm{r}}_2>$ C implies no emergent ray.