Refraction

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A2 = ArcTan[i3 - i2, j3 - j2]

A1 = ArcTan[i2 - i1, j2 - j1]

A0 = ArcTan[i1 - i0, j1 - j0] <br />

T2 = ArcTan[n2 - i2, m2 - j2]

T1 = ArcTan[n1 - i1, m1 - j1] <br />

B2 = A1 - Pi

B1 = A0 - Pi

A2>0, T2>0, B2>0, Q2>0, R2>0<br />

Q2 = A2 - T2

R2 = Pi - T2 - (-B2) = Pi - T2 + B2<br />

Sin[Q2] = n Sin[R2]

Sin[A2 - T2] = n Sin[Pi - T2 + B2]

Sin[T2 - A2] = n Sin[B2 - T2]

Sin[A2 - T2] = n Sin[A1 - T2]

A2 = T2 + ArcSin[n Sin[A1 - T2]]

A1>0, T1>0, B1>0, Q1>0, R1>0<br />

Q1 = A1 - T1

R1 = Pi - T1 - (-B1) = Pi - T1 + B1<br />

n Sin[Q1] = Sin[R1]

n Sin[A1 - T1] = Sin[Pi - T1 + B1]

n Sin[A1 - T1] = -Sin[B1 - T1]

n Sin[T1 - A1] = Sin[B1 - T1] <br />

n Sin[A1 - T1] = Sin[A0 - T1]

A1 = T1 + ArcSin[Sin[A0 - T1]/n]

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