Concept explainers
(a)
The angle of the second order ray in diffraction grating.
(a)
Answer to Problem 60P
The angle of the second order ray in the diffraction grating that has
Explanation of Solution
Given info: The number of grooves per
Formula to calculate angle of
Here,
First calculate the grid spacing, formula to calculate grid spacing is,
Substitute
Substitute
Conclusion:
Therefore, The angle of the second order ray in the diffraction grating that has
(b)
The change in the angle of the second order ray in the diffraction grating if the apparatus is in water.
(b)
Answer to Problem 60P
If the apparatus is submerged in the water the angle of the second order ray in the diffraction grating that has
Explanation of Solution
Given info: The number of grooves per
From equation (1) formula to calculate angle of
Here,
The whole apparatus is now submerged into water therefore the wavelength of the incident light will be reduced to factor of the refractive index of water.
The new incident wavelength is
Here,
Substitute
From equation (6), substitute
Conclusion:
Therefore, if the apparatus is submerged in the water the angle of the second order ray in the diffraction grating that has
(c)
To show: The two diffracted rays from part (a) and part (b) are related through the law of refraction.
(c)
Answer to Problem 60P
The relation between the diffracted rays for the part (a) and part b is
Explanation of Solution
for the part (a) from equation (1),
For second order ray substitute
From equation (4) for the second part when the apparatus is submerged in water,
Form equation (5) Substitute
For second order, ray substitute
Compare equation (8) and (10).
Substitute
Here,
From equation (11), it is evident that it can be expressed in terms of law of refraction.
Conclusion:
Therefore, the two diffracted rays of part (a) and part (b) is related through law of refraction.
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Chapter 27 Solutions
Principles of Physics: A Calculus-Based Text
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