All Problems

Dispersion and Absorption of Light

Problem 5.214

Two plates, one of thickness d1=3.8 mmd_{1}=3.8 \mathrm{~mm} and the other of thickness d2=9.0 mm,d_{2}=9.0 \mathrm{~mm}, are manufactured from a certain substance. When placed alternately in the way of monochromatic light, the first transmits τ1=0.84\tau_{1}=0.84 fraction of luminous flux and the second, τ2=0.70.\tau_{2}=0.70 . Find the coefficient of linear absorption of that substance. Light falls at right angles to the plates. The secondary reflections are to be neglected.

Reveal Answer
x=ln(τ1/τ2)d2d1=0.35 cm1x=\frac{\ln \left(\tau_{1} / \tau_{2}\right)}{d_{2}-d_{1}}=0.35 \mathrm{~cm}^{-1}