Concept explainers
(a)
The proof that total deviation of a ray from its original path is
(a)
Answer to Problem 124PQ
The total deviation of a ray from its original path is
Explanation of Solution
Write the expression for refraction law at left side of the given prism.
Here,
Write the expression for refraction law at right side of the given prism.
Here,
Write the expression angle of deviation of the given prism.
Here,
Write the relation among various angle from the geometry of the prism.
Substitute
Further solve this for
Use general trigonometric relation for conversion.
Substitute
Substitute
Substitute
Conclusion:
Therefore, it is proved that the angle of deviation is
(b)
The plot of the angle of deviation versus the angle of incidence for
(b)
Answer to Problem 124PQ
The graph is following.
Explanation of Solution
Write the expression for the angle of deviation of the given prism.
Conclusion:
Substitute
Deviation varies linearly, decreases and then increases approximately with incidence angle
Therefore, the plot of the angle of deviation versus the angle of incidence is as follows.
Figure-(1)
(c)
The incidence angle for which the derivation angle is minimum.
(c)
Answer to Problem 124PQ
The incidence angle for which deviation is minimum is
Explanation of Solution
The minimum deviation occurs when the incident and the refracted ray are identical and make equal angles to the normal of the prism.
The angle exhibits a minimum at
Conclusion:
The minimum angle of deviation depends on the refractive index for different wavelength, the refractive index is different.
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Chapter 38 Solutions
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