Concept explainers
(a)
To show that the phase difference between the waves from two adjacent slits is given by
(a)
Explanation of Solution
Given:
The path difference is calculated by considering two slits separated by a distance
Formula used:
Write the equation of sinusoidal wave coming from first slit.
Here,
Write the path difference of a sinusoidal wave is given as
Here,
Calculation:
A sine wave repeats itself after a regular interval of
Suppose two waves having same phase initially travel different distances
Here,
Substitute
Conclusion:
Thus, phase difference is given as
The differentiated form of phase difference is given by
Explanation of Solution
Given:
The phase difference of two waves is given as
Formula used:
Write the differentiateof
Rearrange the above equation.
Calculation:
Differentiate the equation (1).
Substitute
Conclusion:
Thus,the differentiatedform of phase difference is given by
The angular separation between the intensity maximum and minimum for some wavelength is
Explanation of Solution
Given:
The angular separation between an interference maximum and an interference minimum corresponds to a phase change of
Formula Used:
Write the differentiate of phase difference is given by
Calculation:
Substitute
Rearrange the above equation.
Conclusion:
Thus, the angular separation between the intensity maximum and minimum for some wavelength is
(d)
The angular separation of the
(d)
Explanation of Solution
Given:
The angle of
Formula used:
Write the differentiation of
Rearrange the above equation.
Calculation:
Differentiate equation (5).
Substitute
Conclusion:
Thus,the angular separation of the
The resolving power is given as
Explanation of Solution
Given:
The angular separation of the
The angular separation between the intensity maximum and minimum for some wavelength is
Formula Used:
The resolving power of a grating is given by
Calculation:
Equate equation (7) and equation (8).
Rearrange the above equation.
Conclusion:
Thus,the resolving power is given as
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Chapter 33 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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