Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 35 - Interference - Problems - Page 1077: 73

Answer

140 bright fringes are formed along the film’s length.

Work Step by Step

The first bright fringe on the left end will be a result of the wave bouncing off the lower edge of the air wedge undergoing an additional phase shift of $\lambda/2$ due to the path difference. I.e., $2d_1={\lambda\over 2}$ Where $d_1$ is the wedge height at the point of incidence of the light ray. Whereas on the opposite end where the wedge height is $d_2$, the formation of the last bright fringe requires, $2d_2=(m+{1\over 2}\lambda)$ Where, the total number of bright fringes is $m+1$. Subtracting the above two equations, \begin{align*} 2(d_2-d_1)&=m\lambda\\ m&={2(d_2-d_1)\over\lambda}\\ &=2\times {48\times 10^{-6}\over 683\times 10^{-9}}\\ &=140.5 \end{align*} Hence, a total of 140 bright fringes are formed along the film’s length.
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