Concept explainers
(a)
The width of aperture.
(a)
Answer to Problem 4P
The width of aperture is
Explanation of Solution
On looking at the figure P38.4, width of the rectangular patch is more than that of its height.
Write the equation for tangent of angular width of aperture.
Here,
Since
Write the relation between width of aperture and the wavelength of light used for first order diffraction pattern.
Here,
Conclusion:
Substitute
Substitute
Rewrite the above expression in terms of
Therefore, the width of aperture is
(b)
The height of aperture.
(b)
Answer to Problem 4P
The height of aperture is
Explanation of Solution
On looking at the figure P38.4, width of the rectangular patch is more than that of its height.
Write the equation for tangent of angular width of aperture.
Here,
Since
Write the relation between width of aperture and the wavelength of light used for first order diffraction pattern.
Here,
Conclusion:
Substitute
Substitute
Rewrite the above expression in terms of
Therefore, the height of aperture is
(c)
Check whether the horizontal or vertical dimension of central bright portion is greater.
(c)
Answer to Problem 4P
Horizontal dimension of central bright portion is longer than its vertical dimension.
Explanation of Solution
Draw the diagram showing the diffraction pattern on light passing through a circular aperture.
From the diagram, it can be seen that the central bright patch has an ellipse shape. It has greater length in horizontal direction than in vertical direction.
Therefore, the horizontal dimension of central bright portion is longer than its vertical dimension.
(d)
Check whether the horizontal or vertical dimension of aperture is greater.
(d)
Answer to Problem 4P
Vertical dimension of aperture is greater.
Explanation of Solution
Refer the diagram shown in part (c). From the diagram, it is understood that to obtain diffraction pattern with greater horizontal dimension its vertical length, the vertical length of aperture must be greater than that of horizontal length. If the horizontal dimension of aperture is greater, the vertical dimension of bright becomes greater than that of the horizontal dimension.
Therefore, the vertical dimension of aperture is greater.
(e)
Identify the relation between the two rectangles given in question with the help of a diagram.
(e)
Answer to Problem 4P
The distances between edges of rectangular aperture is inversely proportional to size of central maxima rectangle on the wall.
Explanation of Solution
Refer the figure 1shown in part (c). The size of aperture is inversely proportional to the size of diffraction pattern. Smaller the size of aperture, larger will be the size of diffraction pattern. It is found that the width of aperture is
Therefore, the distances between edges of rectangular aperture is inversely proportional to size of central maxima rectangle on the wall.
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Chapter 38 Solutions
Physics for Scientists and Engineers With Modern Physics
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