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Question

When light rays are incident on a prism at an angle of 45o, the minimum deviation is obtained. If the refractive index of the material of the prism is 2, then the angle of prism will be
  1. 30o
  2. 45o
  3. 60o
  4. 90o

A
45o
B
90o
C
30o
D
60o
Solution
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Letidenoteincidenceangleandrdenoterefractedangle.Given:i=2×rNowbysnellsLawapplingatinterfaceofism:sinisinr=sin(2r)sinr=2sinr×cosrsinr=2cosr=2wherewehaveusedtrignometricidentity;sin2r=2sinx×cosxThereforewehave;cosr=22=12r=450nowwehave3relationfromaminimumdeviation;A=r1+r2A=2rA=900

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