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Two transparent slabs have the same thic...

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

A

1.1

B

1.2

C

1.3

D

1.4

Text Solution

Verified by Experts

The correct Answer is:
C
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 `
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