For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies.

Question

Accepted Answer

Correct answer: C. (c) At minimum deviation, _m=A (angle of minimum deviation equals prism angle). The refractive index formula becomes: n= sin ( A+ _m2 ) sin ( A2 )= sin ( 2A2 ) sin ( A2 )= sinA sin ( A2 )Using sinA=2 sin ( A2 ) cos ( A2 ) : n= 2 sin ( A2 ) cos ( A2 ) sin ( A2 )=2 cos ( A2 )For a physical prism, 0<A<90^ , so 45^ < A2<90^ , giving 0< cos ( A2 )< 1 2. Therefore, 1<n< 2 2=2 2. However, more precisely, 2<n<2.

$For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index of the prism satisfies.$

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