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The figure depicts a simplistic optical fiber: a plastic core (n_1 = 1.58) is surrounded by a plastic sheath (n_2 = 1.44). A light ray is incident on one end of the fiber at angle theta. The rays is to undergo total internal reflection at point A, where it encounters the core-sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of theta that allows total internal reflection at A?

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The critical angle for total internal reflection at A is sin?1(1.44/1.58) = 65.698 deg

. Using trigonometry, the angle
at the air/glass interface is thus 90 ? 65.698= 24.302

. Using Snell’s law, 1 sin(theta) = 1.58* sin(24.302), the maximum value of

theta that allows total internal reflection at A is 40.54 deg

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