Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 29 - Think and Discuss: 64

Answer

Wider-spaced fringes are seen in air.

Work Step by Step

In water, the wavelengths of light are compressed (see Figure 28.25). In Figure 29.18, the bright fringes are seen when there is a full-wavelength difference in path lengths from the two slits. With a compressed wavelength, one does not have to go as far from the centerline to have a full-wavelength path difference, so the pattern is compressed and the fringes are closer together. The widely-spaced fringes are seen when the experiment is carried out in air. Alternatively, the equation at the bottom of page 550 explains this. $$\lambda = d sin \theta$$ In air, we have a longer wavelength, $\lambda$. The left-hand side of the equation is larger, so the right-hand side must be larger too. The distance between the slits, d, is fixed. The longer wavelength in air gives a more spread-out pattern, i.e., $\theta$ increases, because sin $\theta$ increases.
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