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 up 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 waves inside both, the refractive index of B is

• A. 1.1
• B. 1.2
• C. 1.3
• D. 1.4

Answer 1

The correct option is C 1.3

$\left(Totalnumberofwaves\right)=\left(\frac{opticalpathlength}{wavelength}\right)Opticalpathlength=refractiveindex\times thicknessForAtotalnumberofwaves=\frac{1.5\times t}{\lambda }\left(i\right)ForBandCtotalnumberofwaves=\frac{n_B\times \left(\frac{t}{3}\right)}{\lambda }+\frac{1.6\times \left(\frac{2t}{3}\right)}{\lambda }\left(ii\right)Equating\left(i\right)and\left(ii\right)weget{n}_B=1.3$