A ray of light passes through four transparent media with refractive indices`mu_1`,`mu_2`,`mu_3` and `mu_4` as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have

Options

A. `mu_1=mu_2`
B. `mu_2=mu_3`
C. `mu_3=mu_4`
D. `mu_4=mu_1`

Answer

D

Explanation

Applying Snell's law at P,
`1_(mu_2)=(sin_i)/(sin_(r1))=(mu_2)/(mu_1)`
Applying Snell's law at Q,
`2_(mu_3)=(sinr_1)/(sinr_2)=(mu_3)/(mu2)`…(2)
Again applying Snell's law at R
`3_(mu_4)=(sinr_2)/(sini)=(mu_4)/(mu_3)` …(3)
Multiplying(i),(ii)and (iii), we get `mu_4=mu_1`
NOTE: If the emergent ray is parallel to incident ray after travelling a number of parallel interfaces then the refractive index of the first and the last medium is always same.