Concept explainers
Suppose the single slit in Figure 38.4 is 6.00 cm wide and in front of a microwave source operating at 7.50 GHz. (a) Calculate the angle for the first minimum in the diffraction pattern. (b) What is the relative intensity l/lmax at 0 =- 15.0°? (c) Assume two such sources, separated laterally by 20.0 cm, are behind the slit. What must be the maximum distance between the plane of the sources and the slit if the diffraction patterns are to be resolved? In this case, the approximation sin θ ≈ tan 8 is not valid because of the relatively small value of a/λ.
(a)
The angle for the first minimum in the diffraction pattern.
Answer to Problem 38.77CP
The angle for the first minimum in the diffraction pattern is
Explanation of Solution
Given info: The width of the slit is
The expression of wavelength (
Here,
Substitute
Thus, the wavelength of the microwave source is
The expression of the condition for the first minimum in the diffraction pattern is,
Here,
Substitute
Thus, the angle for the first minimum in the diffraction pattern is
Conclusion:
Therefore, the angle for the first minimum in the diffraction pattern is
(b)
The relative intensity at
Answer to Problem 38.77CP
The relative intensity at
Explanation of Solution
Given info: The width of the slit is
The expression of the intensity variation in a diffraction pattern from a single slit is,
Here,
Rearrange the above equation for
Substitute
Thus, the relative intensity
Conclusion
Therefore, the relative intensity at
(c)
The maximum distance between the plane of the sources and the slit if the diffraction pattern are to be resolved.
Answer to Problem 38.77CP
The maximum distance between the plane of the sources and the slit if the diffraction pattern are to be resolved is
Explanation of Solution
Given info: The width of the slit is
The figure1 shows the given condition.
Figure (1)
Consider
The expression of distance (
Here,
Substitute
Thus, the distance of each source from the central line is
From figure1 the expression of distance (
The value of angle
Substitute
Substitute
Conclusion:
Therefore, The maximum distance between the plane of the sources and the slit if the diffraction pattern are to be resolved is
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Chapter 38 Solutions
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