Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 22 - Wave Optics - Conceptual Questions - Page 648: 8

Answer

(a) The circular spot of light on the screen increases in diameter. (b) The circular spot of light on the screen decreases in diameter.

Work Step by Step

We can write an equation for width of the central maximum: $w = \frac{2.44~\lambda~L}{d}$ (a) In order for diffraction to occur, the light wavelength must be of the order of the aperture diameter. Since green light has a wavelength of about $550~nm$, it is not of the order of the aperture width which is $d = 100~mm$ Thus the light on the screen will be proprtional to the diameter of the aperture. If the hole diameter is increased by $20\%$, then the circular spot of light on the screen increases in diameter. (b) In order for diffraction to occur, the light wavelength must be of the order of the aperture diameter. Since green light has a wavelength of about $550~nm$, it is of the order of the aperture width which is $d = 100~\mu m$. Thus diffraction will occur. If the hole diameter is increased by $20\%$, then the circular spot of light on the screen decreases in diameter.
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