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Discussion Response Post to: Why refraction occur due to change in speed of light or going from one medium to another?

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edison (8935)

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Fermat's Principle:Reflection

Fermat's Principle: Light follows the path of least time. The law of reflection can be derived from this principle as follows:

The pathlength L from A to B is

Since the speed is constant, the minimum time path is simply the minimum distance path. This may be found by setting the derivative of L with respect to x equal to zero.

This derivation makes use of the calculus of max-min determination, the derivative of a square root, and the definitions of the triangle trig functions.

Fermat's Principle and Refraction

Fermat's Principle: Light follows the path of least time. Snell's Law can be derived from this by setting the derivative of the time =0. It shows how the refraction of light at an interface depends upon the indices of refraction.

A paradox is an argument that starts with apparently acceptable assumptions and leads by apparently valid deductions to an apparent contradiction. Since logic admits no contradictions, either the apparently acceptable assumptions are not acceptable, or the apparently valid deductions are not valid, or the apparent contradiction is not a contradiction. A paradox moves us to reexamine the argument until we find out what is wrong.

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Fermat's Principle:Reflection

Fermat's Principle and Refraction

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