Concept explainers
(a)
The number of orders of lines that can be seen with the grating.
(a)
Answer to Problem 45P
The number of orders of lines that can be seen with the grating is
Explanation of Solution
Given that the width of the grating is
Write the expression for the slit width of the grating.
Here,
Write the expression for the diffraction maxima using grating.
Here,
Deduce the number of orders that can be seen, from equation (II).
The maximum number of orders is obtained for
Conclusion:
Substitute
Substitute
Since
Therefore, the number of orders of lines that can be seen with the grating is
(b)
The angular separation
(b)
Answer to Problem 45P
The angular separation
Explanation of Solution
Given that the width of the grating is
Solve equation (II) for
The angles corresponding to each wavelengths for each orders can be computed and their difference gives the angular separation.
Conclusion:
The value of
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Compute the angular separation for each orders.
Therefore, the angular separation
(c)
The order of the spectrum which best resolves the two lines.
(c)
Answer to Problem 45P
The third order spectrum best resolves the two lines.
Explanation of Solution
The angular separation for different orders of the spectrum are obtained as
The higher resolution corresponds to larger angular separation in the diffraction process. Among the obtained values of the angular separations, the third order spectrum has the largest angular separation. Thus, the two lines are best resolved in the third-order spectrum.
Conclusion:
Therefore, the third order spectrum best resolves the two lines.
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