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I'm confused about why we only differentiate with respect to the X when deriving Snell's law. Can someone explain why we do not also do a differentiation with respect to Y.

For more clarification about the question please see the following screenshots:

simple diagram of ray entering a different medium

enter image description here

My question is why do they only do dt/dx and not dt/dy?

Qmechanic
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Legend27
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1 Answers1

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The value of y is constant in your diagram - namely the front face of the glass. If you had a curved surface you would integrate with respect to both x and y - but here y is constant and the derivative is trivially zero.

Floris
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