A ray of light strikes the midpoint of one face of an equiangular (60°−60°−60°) glass prism (n = 1.5) at an angle of incidence of 30°. (a) Trace the path of the light ray through the glass and find the angles of incidence and refraction at each surface. (b) If a small fraction of light is also reflected at each surface, what are the angles of reflection at the surfaces?
(a)
The trace of path of the light ray through the glass and the angles of incidence and refraction at each surface.
Answer to Problem 25P
The angles of incidence and refraction at surface
Explanation of Solution
Introduction:
When a ray incidents on the glass then the rays get refracted through angle of refraction
Given info: The angle of incidence at surface
The path of the light ray through the glass is shown below,
Figure (1)
Write the Snell’s law, for surface
Here,
Rearrange the above expression for
Substitute
Thus the incidence angle at surface
From the figure, the corresponding angles are equal.
Substitute
From the figure, the alternate angles are equal.
Substitute
From the figure
Substitute
Thus the angle of incidence at surface
Write the Snell’s law, for surface
Here,
Rearrange the above expression for
Substitute
Thus the angle of refraction at surface
Conclusion:
Therefore, the angles of incidence and refraction at surface
(b)
The angles of reflection at each surface.
Answer to Problem 25P
The angle of reflection at surface
Explanation of Solution
Given info: The angle of incidence at surface
From the angle of reflection at surface
Here,
Rearrange the above expression for
Substitute
Thus the angle of reflection at surface
From the angle of reflection at surface
Here,
Rearrange the above expression for
Substitute
Thus the angle of reflection at surface
Conclusion:
Therefore, the angle of reflection at surface
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Chapter 25 Solutions
Principles of Physics: A Calculus-Based Text
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