Concept explainers
Consider a wave passing through a single slit. What happens to the width of the central maximum of its diffraction pattern as the slit is made half as wide? (a) It becomes one-fourth as wide. (b) It becomes one-half as wide. (c) Its width does not change. (d) It becomes twice as wide. (e) It becomes four times as wide.
The effect on width of central maximum on decreasing the size of slit width to half the initial value.
Answer to Problem 1OQ
Option (d)
Explanation of Solution
Write the condition for first order dark central maxima for diffraction produced by wave passing through the slit.
Here,
Write the expression for tangent of
Rewrite the first equation by substituting the above one.
Express
Here,
Rewrite the above expression by substituting equation (I).
Rewrite the expression for
Conclusion:
Rewrite the above equation by replacing
It is found that as slit width reduces to half the initial value, width of central maximum will increases by two times. Thus, option (d) is correct.
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