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(D) The formula for the refractive index of a prism is given by $\mu = \frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \frac{A}{2}}$,where $A$ is the an

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$2 \cos ^{-1}\left(\frac{\mu}{2}\right)$

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(D) The formula for the refractive index of a prism is given by $\mu = \frac{\sin \left(\frac{A+D_m}{2}\right)}{\sin \frac{A}{2}}$,where $A$ is the angle of the prism and $D_m$ is the angle of minimum deviation.Given that $D_m = A$,we substitute this into the formula:$\mu = \frac{\sin \left(\frac{A+A}{2}\right)}{\sin \frac{A}{2}}$$\mu = \frac{\sin A}{\sin \frac{A}{2}}$Using the trigonometric identity $\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$,we get:$\mu = \frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}}$$\mu = 2 \cos \frac{A}{2}$$\frac{\mu}{2} = \cos \frac{A}{2}$$\frac{A}{2} = \cos ^{-1}\left(\frac{\mu}{2}\right)$$A = 2 \cos ^{-1}\left(\frac{\mu}{2}\right)$

$A$ glass prism having a refractive index $\mu$ is placed in air. If the angle of minimum deviation of the prism is equal to the angle of the prism,what is the value of the angle of the prism?

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