The refractive index of a prism with apex angle A is cot(A)/(2) ....

As we know, $\mu = \dfrac{\sin \left(\dfrac{A + {\delta}_{m}}{2}\right)}{sin\dfrac{A}{2}}$

$⇒ \dfrac{cos\dfrac{A}{2}}{sin\dfrac{A}{2}} = \dfrac{\sin \left(\dfrac{A + {\delta}_{m}}{2}\right)}{sin\dfrac{A}{2}}$

$⇒ \sin \left(\dfrac{\pi}{2} - \dfrac{A}{2}\right) = \sin \left(\dfrac{A + {\delta}_{m}}{2}\right)$

$⇒ \dfrac{\pi}{2} - \dfrac{A}{2} = \dfrac{A}{2} + \dfrac{{\delta}_{m}}{2}$

$⇒ {\delta}_{m} = \pi - 2A = 180 ° - 2A$