Concept explainers
White light is incident on a diffraction grating that has 2.85 × 103 rulings per centimeter, producing first-order maxima at 6.55°, 8.75°, and 11.2°.
a. What are the wavelengths responsible for these three first-order maxima?
b. At which angles do these wavelengths produce second-order maxima?
(a)
The wavelength responsible for the three first-order maxima.
Answer to Problem 62PQ
The wavelength for
Explanation of Solution
A set of equally spaced parallel lines, producing a spectrum by diffraction and interference of light that are used to separate an incident wave front into its component wavelengths is known as diffraction grating.
Write the expression for
Here,
Write the formula for grating spacing.
Here,
Conclusion:
Substitute
Calculate the wavelength for
Substitute
Calculate the wavelength for
Substitute
Calculate the wavelength for
Substitute
Therefore, the wavelength for
(b)
The angles at which the three wavelengths produce second-order maxima.
Answer to Problem 62PQ
The angle at which the second-order maxima occurs due to
Explanation of Solution
Rearrange the equation (I) to find
Conclusion:
Calculate the angle at which the second-order maxima occurs due to
Substitute
Calculate the angle at which the second-order maxima occurs due to
Substitute
Calculate the angle at which the second-order maxima occurs due to
Substitute
Therefore, the angle at which the second-order maxima occurs due to
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Chapter 36 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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