Concept explainers
A spectrum of white light is obtained with a grating ruled with 2500 lines/cm. Compute the angular separation between the violet
(a)
The angular separation between the first order image formed on the screen due to the violet and red wavelength if the spectrum of white light is obtained with a grating rule with
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
The wavelength of the red light
The wavelength of the violet light
The number of lines in the diffraction grating is
The order of the spectrum formed on the screen is
Formula used:
The expression for diffraction grating is written as:
Here,
Rearrange for
The value of
Explanation:
The width of the slit in the diffraction grating is equal to the inverse of the number of lines per unit. Hence, the value of
Rewrite the expression for diffraction grating for the violet light.
Here,
Substitute
Rewrite the expression for diffraction grating for the red light.
Here,
Substitute
The angular separation between the first order image due to the violet and red lights is written as:
Here,
Substitute
Conclusion:
Therefore, the angular separation between the first order image formed on the screen due to the violet and red wavelength is
(b)
The angular separation between the second order image formed on the screen due to the violet and red wavelength if the spectrum of white light is obtained with a grating rule with
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
The wavelength of the red light
The wavelength of the violet light
The number of lines in the diffraction grating is
The order of the spectrum formed on the screen is
Formula used:
The expression for diffraction grating is written as:
Here,
The value of
Explanation:
Rewrite the expression for diffraction grating for the violet light.
Here,
Substitute
Rewrite the expression for diffraction grating for the red light.
Here,
Substitute
The angular separation between the second order image due to the violet and red lights is written as:
Here,
Substitute
Conclusion:
Therefore, the angular separation between the second order image formed on the screen due to the violet and red wavelength is
(c)
Whether the yellow light (
Answer to Problem 39SP
Solution:
Explanation of Solution
Given data:
The wavelength of the yellow light
The order of spectrum on the screen is third order.
The wavelength of the violet light
The order of spectrum on the screen is fourth order.
The number of lines in the diffraction grating is
Formula used:
The expression for diffraction grating is written as:
Here,
The value of
Explanation:
Rewrite the expression for diffraction grating for the yellow light.
Here,
Substitute
Rewrite the expression for diffraction grating for the violet light.
Here,
Substitute
The angular separation between the third order image due to the violet and yellow lights is written as:
Here,
Substitute
Conclusion:
Therefore, the angular separation between the thirdorder image formed on the screen due to the yellow wavelength and the fourth order image formed on the screen due to the violet wavelength is
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Chapter 40 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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