Three transparent media A, B and C are such that the speeds of light in them satisfy vA:vB:vC=1:1.5:2. Answer the following questions.
a. (i) Express the refractive indices nA, nB and nC in terms of a common constant and arrange them in ascending order.
b. (ii) If a ray of light travels from medium A into medium C across a plane boundary, discuss whether total internal reflection is possible. Give the necessary condition to support your answer.
c. (iii) For light travelling from medium A to medium B, derive an expression for the critical angle in terms of vA and vB, and calculate its numerical value using the given ratio.