A plane glass disk with a small thickness d, is used to re-image the laser spot O into the center O' of an optical fiber (fiber coupling). Show that for perfect imaging from a finite object distance / to finite image distance l' perfect requires that glass disk has gradual variation in its refractive index such that h n(h) = n, 2d, f" where n, is refractive index on axis and f' is the back focal length. Hint: apply Fermat's principle of stationary optical path and formula 1 1 1 ---%3D do

Principles of Physics: A Calculus-Based Text
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Author:Raymond A. Serway, John W. Jewett
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Chapter26: Image Formation By Mirrors And Lenses
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Homework Problem 4
A plane glass disk with a small thickness d, is used to re-image the laser spot O
into the center O' of an optical fiber (fiber coupling).
Show that for perfect imaging from a finite object distance / to finite image
distance l' perfect requires that glass disk has gradual variation in its refractive
index such that
n(h) x n,
2d, f"
where n, is refractive index on axis and f' is the back focal length.
Hint: apply Fermat's principle of stationary optical path and formula
1
----%3D
Transcribed Image Text:Homework Problem 4 A plane glass disk with a small thickness d, is used to re-image the laser spot O into the center O' of an optical fiber (fiber coupling). Show that for perfect imaging from a finite object distance / to finite image distance l' perfect requires that glass disk has gradual variation in its refractive index such that n(h) x n, 2d, f" where n, is refractive index on axis and f' is the back focal length. Hint: apply Fermat's principle of stationary optical path and formula 1 ----%3D
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