A ray of light intensity I is incident on a parallel glass-slab at a point `A` as shown in figure. It undergoes partial reflection and refraction. At each reflection `25%` of incident energy is reflected. The rays `AB` and `A^(')B^(')` undergo interference. The ratio `I_(max)//I_(min)` is

Options

A. `4 : 1`
B. `8 : 1`
C. `7 : 1`
D. `49 : 1`

Answer

D

Explanation

Intensity reflected along `AB, I_(1) = I//4`
Intensity transmitted along `AC = 3I//4`
Intensity reflected along `CA' = (1)/(4) xx (3I)/(4) = 3 I//16`
Intensity reflected transmitted along
`A'B' = I_(2) = (3 I)/(16) - (3I)/(64) = (9 I)/(64)`
`(I_(1))/(I_(2)) = (a^(2))/(b^(2)) = (I)/(4) xx (64)/(9 I) = (16)/(9) :. (a)/(b) = (4)/(3)`
`(I_(max))/(I_(min)) = (a + b)^(2)/(a - b)^(2) = (4 + 3)^(2)/(4 - 3)^(2) = (49)/(1)`