Concept explainers
Suppose the slit width in Figure 37.4 is made half as wide. Does the central bright fringe (a) become wider, (b) remain the same, or (c) become narrower?
Figure 37.4 (a) Geometry for analyzing the Fraunhofer diffraction pattern of a single slit. (Drawing not to scale.) (b) Simulation of a single-slit Fraunhofer diffraction pattern.
Answer to Problem 38.1QQ
Explanation of Solution
Consider the figure given below.
Figure (1)
The condition for the central diffraction maximum is,
Here;
From the figure (1),
Here
From the trigonometry property, for very small angle,
Substitute
Substitute
For the case of central bright fringe, the order of the fringe is
Substitute
For
Rearrange the above equation for
Thus from above equation the central bright fringe width is inversely proportional to the slit width. Thus, if the slit width decreases or half of the initial value the width of central bight fringe increases.
Conclusion:
The width of the central bright fringe is inversely proportional to the slit width so, if the slit width decreases the width of central bright fringe increases. Thus option (a) is correct.
The slit width is half of the initial value and there is inverse dependence of width of central maxima and slit width so decrease in slit width widens the central bright fringe. Thus option (b) is incorrect.
The width of the central bright fringe is inversely proportional; so decrease in slit width will increase width. Thus option (c) is incorrect.
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Chapter 38 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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