Concept explainers
(a)
The number of wavelengths present in the spectrum of the light source.
(a)
Answer to Problem 43P
There are two spectral lines with wavelengths
Explanation of Solution
Write the expression to calculate the slit width.
Here, d is the slit width and n is the number of slits.
Substitute
Write the expression to calculate the first order wavelength for the smallest angle.
Here,
Substitute
Write the expression for the angle of second order lines for the above wavelength.
Substitute
Write the expression for the angle of third order lines for the above wavelength.
Substitute
Write the expression for the angle of fourth order lines for the above wavelength.
Substitute
Thus, these angles belong to the second order wavelengths and these angles could be omitted.
Write the expression to calculate the first order wavelength for the angle
Substitute
Write the expression for the angle of second order lines for the above wavelength.
Substitute
Write the expression for the angle of third order lines for the above wavelength.
Substitute
Thus, the angle corresponding the wavelength could be omitted.
Conclusion:
Therefore, there are two spectral lines with wavelengths
(b)
The number of spectral lines on one side of the central maximum.
(b)
Answer to Problem 43P
The number of spectral lines is
Explanation of Solution
Write the expression to calculate the slit width.
Here, d is the slit width and n is the number of slits.
Substitute
Write the expression to calculate order corresponding to the wavelength
Substitute
Write the expression to calculate order corresponding to the wavelength
Substitute
Thus, the total number of spectral lines is
Conclusion:
Therefore, the number of spectral lines is
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Chapter 25 Solutions
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