题干

将长为l的玻璃圆柱体沿轴剖开后得到一块半圆柱体,其截面的正视图如图所示,MNPQ为其底面(PQ图中未画出),MN为直径.已知半圆的圆心为O、半径为R,玻璃的折射率n= 2 .一束与MNPQ所在平面成45°且垂直于轴的平行光束射到半圆柱面上,经折射后,有部分光能从MNPQ面射出,忽略经多次反射到达MNPQ面的光线,求MNPQ透光部分的面积.
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解:设光由介质射向空气的临界角为C.

由 sinC=

1
n
,得 C=45°

从A点进入玻璃砖的光线垂直半球面,沿半径AO直达球心O,且入射角等于临界角,恰好在O点发生全反射,A点左侧的光线经球面折射后,射在MN上的入射角

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