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: (A) 180^0 - 2A (B) 90^0 - 2A (C) 180^0 + 2A (D) 180^0 - 3A

Here,

μ = cot (A/2)

According to prism formula,

\(\mu = \frac{sin\frac{A+\delta _{m}}{2}}{sin\frac{A}{2}}\\\mu = \frac{cos \frac{A}{2}}{sin\frac{A}{2}}\)

Therefore,

\(sin \frac{A+\delta _{m}}{2}= cos\frac{A}{2}=sin(90^{0}-\frac{A}{2})\\\frac{A+\delta _{m}}{2}=90^{0}-\frac{A}{2}\)

or

\(\delta _{m}=(180^{0}-2A)\)

Hence, the correct option is (A) 

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