Two transparent slabs have the same thickness. One is made of material X of refractive index 1.5. The other is made of two material Y and Z having thickness in the ratio 1:2. The refractive index of Z is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both, the refractive of Y is

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1.2

1.1

1.3

1.4

answer is C.

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Detailed Solution

Wavelength of light in $X = \frac{λ}{1.5}, in Y = \frac{λ}{μ}, in Z = \frac{λ}{1.6}$

$λ$ is wavelength in air

Number of wavelengths in X= number of wavelengths in Y+ number of wavelengths in Z

$\begin{array}{l} \frac{t}{λ / 1 .5} = \frac{t / 3}{λ / μ} + \frac{2 t / 3}{λ / 1 .6} \\ 1 .5 = \frac{μ}{3} + \frac{3 .2}{3} \\ \Rightarrow \frac{μ}{3} = 1 .5 - \frac{3 .2}{3} = \frac{1 .3}{3} \Rightarrow μ = 1 .3 \end{array}$

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