Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive

Question

Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials 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 $\frac{10 + x}{10}$ . Then x is :

Slab A (1.5) and slab of B and C (1.6) of equal thickness

Answer:

3

Solution:

Same number of wavelengths means equal optical path.

$1.5 t = μ_{B} \frac{t}{3} + 1.6 \times \frac{2 t}{3}$

$4.5 = μ_{B} + 3.2$

$μ_{B} = 1.3 = \frac{10 + x}{10}$

$x = 3$

TestHub · Accepted Answer

Same number of wavelengths means equal optical path. 1.5 t = μ B ​ 3 t ​ + 1.6 × 3 2 t ​ 4.5 = μ B ​ + 3.2 μ B ​ = 1.3 = 10 10 + x ​ x = 3

Physics - Geometrical Optics Question with Solution | TestHub

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