Concept explainers
Consider a horizontal interface between air above and glass of index of refraction 1.55 below. (a) Draw a light ray incident from the air at angle of incidence 30.0°. Determine the angles of the reflected and refracted rays and show them on the diagram. (b) What If? Now suppose the light ray is incident from the glass at an angle of 30.0°. Determine the angles of the reflected and refracted rays and show all three rays on a new diagram. (c) For rays incident from the air onto the air–glass surface, determine and tabulate the angles of reflection and refraction for all the angles of incidence at 10.0° intervals from 0° to 90.0°. (d) Do the same for light rays coming up to the interface through the glass.
(a)
Answer to Problem 32AP
Explanation of Solution
Given info: The index of refraction of glass is
From, law of reflection, the angle of incidence is equal to the angle of reflection.
Thus, angle of reflection is
From Snell’s law,
Here,
Substitute
The figure below shows the angle of incidence, the angle of reflection and the angle of refraction.
Figure (1)
Conclusion:
Therefore, the angle of reflection is
(b)
Answer to Problem 32AP
Explanation of Solution
Given info: The index of refraction of glass is
From, law of reflection, angle of incidence is equal to angle of reflection.
Thus, angle of reflection is
From, Snell’s law,
Here,
Substitute
The figure below shows the angle of incidence, the angle of reflection and the angle of refraction.
Figure (2)
Conclusion:
Therefore, the angle of reflection is
(c)
Answer to Problem 32AP
Angle of incidence | Angle of reflection | Angle of refraction |
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Explanation of Solution
From, law of reflection, the angle of reflection is equal to the angle of incidence. So for all value of angles between
The formula to calculate the angle of refraction is,
From, Snell’s law,
Substitute
Substitute
The remaining values of the angle of refraction can be calculated by the same method.
The table for angle of reflection and angle of refraction for all angles of incidence at
Angle of incidence | Angle of reflection | Angle of refraction |
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Conclusion:
Therefore, the angle of reflection is same as the angle of incidence and the of angle of refraction for rays incident from air onto the air-glass surface is increasing as angle of incidence is increasing.
The table for angle of reflection and angle of refraction for all angles of incidence at
Angle of incidence | Angle of reflection | Angle of refraction |
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(d)
Answer to Problem 32AP
The table for angle of reflection and angle of refraction for all angles of incidence at
Angle of incidence(
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Angle of reflection(
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Angle of refraction(
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Explanation of Solution
From, the law of reflection, angle of reflection is equal to the angle of incidence. So, for all value of angles between
The formula to calculate the angle of refraction is,
From, Snell’s law,
Substitute
Substitute
The remaining values of the angle of refraction can be calculated by the same method.
The formula to calculate the critical angle is,
Here,
Substitute
The angle of incidence is greater than
The table for angle of reflection and angle of refraction for all angles of incidence at
Angle of incidence(
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Angle of reflection(
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Angle of refraction(
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Conclusion:
Therefore, the angle of reflection is same as the angle of incidence and the of angle of refraction for rays coming up to the interface through the glass will increase up to angle of incidence
The table for angle of reflection and angle of refraction for all angles of incidence at
Angle of incidence(
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Angle of reflection(
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Angle of refraction(
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Want to see more full solutions like this?
Chapter 34 Solutions
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