(a) A ray of light of wavelength $\lambda$ falls normally on a right-angled isosceles prism $ABC$ of refractive index $n$.

Find the minimum value of refractive index $n$ of the prism required for the total internal reflection of the light to occur on the face $BC$of the prism.

(b) For any given thin prism of small angle $A$, refractive index $n$, and an incident blue light, answer the following questions.

i. Write the formula for angle of minimum deviation for a thin prism. If the whole arrangement is immersed in a liquid of refractive index $n \text{'}<n$, how will the angle of minimum deviation change?

ii. For some angle of incidence on the second face of the prism, the incident blue light undergoes total internal reflection. However, a red incident light for the same angle of incidence on the second face of the prism does not undergo total internal reflection. Give reason.