A point source `S` is placed at the bottom of different layers as shown is figure,the refractive index of bottommost layer is `mu_(0)` The refractive index of any other upper layer is
`mu(n)=mu_(0)-(mu_(0))/(4pi-18)` where `n=1,2,.....`
A ray of light starts form the source `S` as shown. Total internal reflection takes place at the upper surface of a layer haing `n` equal to

Options

A. 3
B. 5
C. 4
D. 6

Answer

A

Explanation

For parallel composite slab `"usin"theta` = constant
`mu_(0) xx "sin"I = mu("n")xx "sin"90^(@)`
`mu_(0) "sin"30^(@) = mu_(0) + (mu_(0))/(mun-18)`
`(1)/(2) = 1 + (1)/(4n-18) implies (1)/(18-4n) = (1)/(2) implies "n"= 4`
`implies` upper layer of n=3