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

For material A
Number of waves `= (n_(A) t)/(lambda) = ("optical path length")/("wavelength") = ((1.5)t)/(lambda)`
For B and C -
Number of waves = `(n_(B) ((t)/(3)) )/(lambda) + (1.6 ((2t)/(3)))/(lambda)`
`rArr (1.5t )/(lambda) = (n_(B) t)/( 3 lambda) + (1.6 xx 2t)/(3 lambda) rArr n_(B) = 1.3 `