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Assuming n₂ ≠ 0
sinx₂ = n₁ sin x₁/n₂ = (n₁/n₂) sin x₁
Next, if we assume that the expression on the far right hand side is bounded between -1 and 1, take the inverse sine to get
x₂ = arcsin((n₁/n₂) sin x₁).
This is about all you can say about x₂ in the absence of any information about the values of x₁ and the two n's.
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Assuming n₂ ≠ 0
sinx₂ = n₁ sin x₁/n₂ = (n₁/n₂) sin x₁
Next, if we assume that the expression on the far right hand side is bounded between -1 and 1, take the inverse sine to get
x₂ = arcsin((n₁/n₂) sin x₁).
This is about all you can say about x₂ in the absence of any information about the values of x₁ and the two n's.