Does the refractive index law change according to the medium

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The refractive index law is expressed as sin(i)/sin(r), but the interpretation of angles i and r can vary based on the medium. The equation can also be represented as sin(α) n_α = sin(β) n_β, where n represents the refractive index of each medium. In the discussed scenario, the angle i corresponds to the light entering water, while angle r relates to the light exiting into air. Consistency in labeling angles is crucial for accurate application of the law. Understanding the context of each medium's refractive index clarifies the relationship between the angles.
Syndy
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The refrative index law should be sine(i)/sine(r) but in the answer he done the opposite. I included the answer in the bottom of the question.
 

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It just depends on what you call i and r and which angle you know.

You can also write it as ##\sin(\alpha) n_\alpha = \sin(\beta) n_\beta## where nα means the refractive index of the medium where you have the angle α and similar for β. Usually, one medium is air with n=1.
 
In the question provided, the i angle is the one from the lamp in the water and the r is the one in the air.

What do you think about the answer I attached? Why is the r angle is the one in the water?!
 
As I said, it does not matter how you call them, you just have to be consistent. n refers to the water, so the sine in the denominator on the other side should use the angle in the water here.
 
Ok. Thank you very much.
 

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