Two transparent slabs have the same thickness as shown in figure. One in made of material A of refractive index 1.5. The other is made of two materilas B and C with thickness in the ratio 1:2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both, the refractive index of B is

Options

A. 1.1
B. 1.2
C. 1.3
D. 1.4

Answer

c

Explanation

Total number of waves `=((1.5)t)/(lambda)`
`("Total number of waves") = (("optical path length")/("wavelength"))`
For B and C:
Total number of waves `=(n_(0) ((t)/(3)))/(lambda) + (1.6((2t)/(3)))/(lambda)`
Equating (i) and (ii), we get
`n_(0) = 1.3`