Physics - Geometrical Optics Question with Solution | TestHub

The refractive index of the material of a prism is given by the prism formula:

$\mu =\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$

For a symmetric (equilateral) prism, the angle of the prism is $A=60^{\circ }$.

Substituting $A=60^{\circ }$ in the formula:

$\mu =\frac{\sin \left(\frac{60^{\circ }+{\delta }_m}{2}\right)}{\sin \left(\frac{60^{\circ }}{2}\right)}$

$\mu =\frac{\sin \left(30^{\circ }+\frac{{\delta }_m}{2}\right)}{\sin (30^{\circ })}$

Since $\sin (30^{\circ })=\frac{1}{2}$, we get:

$\mu =\frac{\sin \left(30^{\circ }+\frac{{\delta }_m}{2}\right)}{\frac{1}{2}}$

$\mu =2\sin \left(30^{\circ }+\frac{{\delta }_m}{2}\right)$

Answer: $2\sin \left(30+\frac{\delta m}{2}\right)$