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Unformatted text preview: glass, the radius from the origin, and the distance x . θ φ x R ' R sin( φ + π/ 2) = x sin φ This gives x = R sin φ sin( φ + π/ 2) = R 1 /n cos φ = R 1 /n q 1-sin 2 θ/n 2 = R p n 2-sin 2 θ . A similar construction on the other side (negative x ) gives R sin(-φ + π/ 2) =-x sin φ This gives-x = R sin φ sin(-φ + π/ 2) = R 1 /n cos φ = R 1 /n q 1-sin 2 θ/n 2 = R p n 2-sin 2 θ , so that the result is symmetric on the two sides of the centerline. This region can extend to the full distance where x = ± R if the denominator is one: p n 2-sin 2 θ = 1 , or sin 2 θ = n 2-1 . The sine can never be larger than one, so this can happen only if n 2 < 2, or n < √ 2....
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- Spring '10
- Total internal reflection, =R =R sin