University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 35 - Interference - Problems - Exercises - Page 1182: 35.31

Answer

110 nm.

Work Step by Step

There is no net phase difference introduced because both rays reflect from identical substrates. The condition for destructive interference is $2t=(m+\frac{1}{2})\lambda$. For the minimum pit depth t, m=0. $$2t=(0+\frac{1}{2})\lambda$$ $$t=\frac{\lambda}{4} $$ Note that $\lambda=\frac{\lambda_0}{1.8}$. $$t=\frac{\lambda_0}{4(1.8)}=\frac{790nm}{4(1.8)}=110 nm $$
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