Concept explainers
A triangular glass prism with apex angle 60.0° has an index of refraction of 1.50. (a) Show that if its angle of incidence on the first surface is θ1 = 48.6°, light will pass symmetrically through the prism as shown in Figure 34.16. (b) Find the angle of deviation δmin for θ1 = 48.6°. (c) What If? Find the angle of deviation if the angle of incidence on the first surface is 45.6°. (d) Find the angle of deviation if θ1 = 51.6°.
(a)
To show: Light will pass symmetrically through the prism if the angle of incidence on the first surface
Answer to Problem 18P
Explanation of Solution
Given information: The apex angle is
The diagram for the given condition is shown below.
Figure (1)
Apply Snell’s law of refraction at the first interface.
The Snell’s law of refraction is,
Here,
Substitute
Apply Snell’s law of refraction at the second interface.
The Snell’s law of refraction is,
Here,
Substitute
Since,
Conclusion:
Therefore, the light will pass symmetrically through the prism.
(b)
Answer to Problem 18P
Explanation of Solution
Given information: The apex angle is
The angle of minimum deviation
Here,
Substitute
Conclusion:
Therefore, the orientation angle in the proper frame is
(c)
Answer to Problem 18P
Explanation of Solution
Given information: The apex angle is
Apply Snell’s law of refraction at the first interface.
The Snell’s law of refraction is,
Here,
Substitute
Apply Snell’s law of refraction at the second interface.
The Snell’s law of refraction is,
Here,
Substitute
The angle of minimum deviation
Here,
Substitute
Conclusion:
Therefore, the orientation angle in the proper frame is
(d)
Answer to Problem 18P
Explanation of Solution
Given information: The apex angle is
Apply Snell’s law of refraction at the first interface.
The Snell’s law of refraction is,
Here,
Substitute
Apply Snell’s law of refraction at the second interface.
The Snell’s law of refraction is,
Here,
Substitute
The angle of minimum deviation
Here,
Substitute
Conclusion:
Therefore, the orientation angle in the proper frame is
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Chapter 34 Solutions
Physics for Scientists and Engineers
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