A slab of transparent material is made as shown in Fig. Monochromatic parallel beams of light are normally incident on the slab. The thickness of `C` is twice the thickness of `B`. If the number of waves in A = number of waves in combination of `B and C`, then the refractive index of `B` is :
.

Options

A. `1.33`
B. `1.8`
C. `1.6`
D. `1.4`

Answer

B

Explanation

Let thickness of `B = t`
`:.` thickness of `C = 2 t`
and thickness of `A = t + 2 t = 3 t`
If `lambda_(0)` is wavelength in air, then as number of waves in `A =` no. of waves in `B +` no. of waves in `C`.
`:. (3 t)/(lambda_(0)//mu_(0)) = (t)/(lambda_(0)//mu_(1)) + (2 t)/(lambda_(0)//mu_(2))`
or `3mu_(0) = mu_(1) + 2 mu_(2)`
or `mu_(1) = 3 mu_(0) - 2 mu_(2)`
`= 3 xx 1.4 - 2 xx 1.2`
`= 1.8`