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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 36 / Problem 23E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Chapter 36, Problem 23E

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QUESTION:

Problem 23E

An interference pattern is produced by light of wavelength 580 nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of 0.530 mm. (a) If the slits are very narrow, what would be the angular positions of the first-order and second-order, two-slit interference maxima? (b) Let the slits have width 0.320 mm. In terms of the intensity I0 at the center of the central maximum, what is the intensity at each of the angular positions in part (a)?

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QUESTION:

Problem 23E

An interference pattern is produced by light of wavelength 580 nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of 0.530 mm. (a) If the slits are very narrow, what would be the angular positions of the first-order and second-order, two-slit interference maxima? (b) Let the slits have width 0.320 mm. In terms of the intensity I0 at the center of the central maximum, what is the intensity at each of the angular positions in part (a)?

ANSWER:

Solution 23E

Intensity maxima of multiple slits is given by $dsin\ \theta{}=m\lambda{}$ , where $d$ is the separation of two identical slits and $\lambda{}$ is the wavelength of light and $m=\ \pm{}1,\ \pm{}2,\ \pm{}3,\ ....$

Given, $\lambda{}=580\ nm=580\times{}1{0}^{-9}\ m$

$d=0.530\ mm=0.530\times{}1{0}^{-3}\ m$

(a) First order maxima,

$m=1$

$0.530\times{}1{0}^{-3}\times{}sin\theta{}=1\times{}580\times{}1{0}^{-9}$

$sin\theta{}=1094/1000000$

$sin\theta{}=0.001094$

$\theta{}=si{n}^{-1}(0.001094)=0.06{3}^{0}$

Therefore, the angular position for the first order maxima is approximately $0.06{3}^{0}$ .

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