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Refraction of light for an Optical Fiber

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The drawing shows an optical fiber that consists of a core made of flint glass(n flint= 1.667) surrounded by a cladding made of crown glass(n crown = 1.523). A beam of light enters the fiber from the air at an angle theta1 with respect to the normal. What is theta1 if the light strikes the core-cladding interface at the critical angle thetac?

(See attached file for full problem description)

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A solution explaining the reaction to light of a core-cladding interface.

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