Chapter 24, Problem 7Q

To determine

To Explain: The difference of path length when two rays of light from the same source destructively interfere.

Answer to Problem 7Q

Because of destructive interference, the path lengths differ by odd half-integer multiples of the wavelength.

Explanation of Solution

Introduction: The pattern resulting from superimposing of two waves is known as interference. Interference can be destructive or constructive.

Destructive interference occurs when the crest of a wave overlaps the trough of another wave. Also, this happens when path length change by odd half integer multiples of $\frac{\lambda }{2},\frac{3\lambda }{2},\frac{5\lambda }{2},\left(m+\frac{1}{2}\right)\lambda$ wavelengths. Under this condition, wave crests from one ray match up with wave troughs from the other ray and also, cancellation occurs (in destructive interference).

Conclusion:  When the crests and troughs match-up, destructive interference occurs.