Refraction

[Graphics:HTMLFiles/index_1.gif]

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

B = ArcTan[i0 - i1, j0 - j1]

T = ArcTan[n1 - i1, m1 - j1]

(Q1≥0, Q2≥0, A≥0, B≥0, T≥0)

Q1 = T - A

Q2 = T - π - B

Sin[Q1] = n Sin[Q2]

Sin[T - A] = n Sin[T - π - B]

Sin[T - A] = n Sin[B - T]

[Graphics:HTMLFiles/index_11.gif]

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

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

A0 = ArcTan[i1 - i0, j1 - j0]

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

T1 = ArcTan[n1 - i1, m1 - j1]

B2 = A1 - π

B1 = A0 - π

Sin[Q2] = n Sin[R2]

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

n Sin[Q1] = Sin[R1]

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