All Problems

Dispersion and Absorption of Light

Problem 5.215

A beam of monochromatic light passes through a pile of N=5N=5 identical plane-parallel glass plates each of thickness ll =0.50 cm.=0.50 \mathrm{~cm} . The coefficient of reflection at each surface of the plates is ρ=0.050.\rho=0.050 . The ratio of the intensity of light transmitted through the pile of plates to the intensity of incident light is τ=0.55\tau=0.55. Neglecting the secondary reflections of light, find the absorption coefficient of the given glass.

Reveal Answer
x=1lNln(1ρ)2Nτ=0.034 cm1x=\frac{1}{l N} \ln \frac{(1-\rho)^{2 N}}{\tau}=0.034 \mathrm{~cm}^{-1}