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. 1.6

Answer

B

Explanation

Let thickness of `B = t`
`:.` Thickness of `C = 2t`
and thickness of `A = t + 2 t = 3 t`
If `lamda_0` is wavelength in air, then as number of waves in `A = no`, waves in `B + no`. Of waves in `C`
`:. (3t)/(lamda_0//mu_0) = (t)/(lamda_0//mu_1) + (2t)/(lamda_0//mu_2)`
or `3 mu_0 = mu_1 + 2mu_2`
or `mu_1 = 3 mu_0 - 2 mu_2`
=`3 xx 1.4 - 2 xx 1.2`
=`1.8`.