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Wave Optics

Question
CBSEENPH12039803
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The refracting angle of a prism is A,  and the refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is

  • 180o-3A

  • 180o-2A

  • 90o-A

  • 180o+2A

Solution

B.

180o-2A

As, we know that,
straight mu space equals fraction numerator sin open parentheses begin display style fraction numerator straight A space plus straight D subscript straight m over denominator 2 end fraction end style close parentheses over denominator sin begin display style straight A over 2 end style end fraction rightwards double arrow space Cot space straight A over 2 space equals space fraction numerator sin open parentheses begin display style fraction numerator straight A space plus straight D subscript straight m over denominator 2 end fraction end style close parentheses over denominator sin begin display style straight A over 2 end style end fraction fraction numerator cos begin display style straight A over 2 end style over denominator sin begin display style straight A over 2 end style end fraction space equals space fraction numerator sin open parentheses begin display style fraction numerator straight A plus straight D subscript straight m over denominator 2 end fraction end style close parentheses over denominator sin begin display style straight A over 2 end style end fraction sin space open parentheses straight pi over 2 minus straight A over 2 close parentheses space equals space sin space open parentheses fraction numerator straight A plus straight D subscript straight m over denominator 2 end fraction close parentheses rightwards double arrow space straight pi over 2 minus straight A over 2 space equals space straight A over 2 plus straight D subscript straight m over 2 straight D subscript straight m space equals space straight pi minus 2 straight A straight D subscript 3 space equals space 180 to the power of straight o minus 2 straight A

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