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

Option: 1

90°-A


Option: 2

180°+ 2A


Option: 3

180°-3A


Option: 4

180°-2A


Answers (1)

best_answer

As we learnt in

Condition of maximum deviation -

i=e

 

 

- wherein

delta _{min}= 2i-A

mu = frac{sin left ( frac{delta _{m}+A}{2} 
ight )}{sin left ( A/2 
ight )}

 

 

\mu= \cot \frac{A}{2}

\because \mu= \frac{sin\frac{A+\delta m }{2}}{\sin \frac{A}{2}}=\cot \frac{A}{2}

or \: \sin \left(\frac{A+\delta m }{2} \right ) =\cos \frac{A}{2}=\sin \left ( 90-\frac{A}{2} \right )

or \: \frac{\delta m +A}{2}=90-\frac{A}{2}=\frac{180-A}{2}

\delta m =180-2A

Posted by

Nehul

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