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With FIXED SOURCE AND RECEIVER, I have a light incident from fluid 1 with velocity v1 into fluid 2 with velocity v2. Obviously, according to Snell's law, v1/v2=sin(alpha1)/sin(alpha2), where alpha1 and alpha2 are the angles with regard to the vertical line.

My question is: how to calculate d(alpha1)/d(v1)?

Obviously, I can obtain the result from numerical calculation, but I am seeking analytical method. I guess maybe I need some approximation to calculate that?

Please note v2 is always constant, please also note when v1 changes, alpha1 and alpha2 change. Please note direct differentiation of Snell's law, I can obtain d(alpha1)/d(alpha2). I am clueless and have already tried several methods but obtain no result, please help!

My question is: how to calculate d(alpha1)/d(v1)?

Obviously, I can obtain the result from numerical calculation, but I am seeking analytical method. I guess maybe I need some approximation to calculate that?

Please note v2 is always constant, please also note when v1 changes, alpha1 and alpha2 change. Please note direct differentiation of Snell's law, I can obtain d(alpha1)/d(alpha2). I am clueless and have already tried several methods but obtain no result, please help!

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