
Concept explainers
(a)
The distance between the adjacent slits on the grating.
(a)

Answer to Problem 65P
The distance between the adjacent slits on the grating is
Explanation of Solution
Given that the number of slits per unit length of the grating is
Write the expression for the distance between adjacent slits.
Here,
Conclusion:
Substitute
Therefore, the distance between the adjacent slits on the grating is
(b)
The distance from the central bright spot to the first-order maximum on the screen.
(b)

Answer to Problem 65P
The distance from the central bright spot to the first-order maximum on the screen is
Explanation of Solution
Given that the
Write the expression for the double slit maxima.
Here,
For, first order spectrum,
Let
From Figure 1, write the expression for
Here,
Use equation (II) in (III).
Conclusion:
Substitute
Therefore, the distance from the central bright spot to the first-order maximum on the screen is
(c)
The distance from the central bright spot to the second-order maximum on the screen.
(c)

Answer to Problem 65P
The distance from the central bright spot to the second-order maximum on the screen is
Explanation of Solution
For, first order spectrum,
Use equation (V) in (III).
Conclusion:
Substitute
Therefore, the distance from the central bright spot to the second-order maximum on the screen is
(d)
Whether the assumption
(d)

Answer to Problem 65P
The assumption
Explanation of Solution
The small angle approximation in trigonometry is used in physical problems, when the angles under consideration are very small. If the angles are considerably large, these approximations cannot be applied.
In the given problem, the angle of diffraction corresponding to the first order diffraction is given by equation (II).
Conclusion:
Substitute
For an angle
Therefore, the assumption
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