Question

What is the dispersive power of the prism and its SI unit?

Answer 1

The dispersive power of a prism:

The dispersive power of a prism would be defined as the difference in refraction of light of the maximum and minimum wavelengths that penetrate or reach the prism. The SI unit of dispersive power of prism is Watt.

Mathematical representation:

Mathematically, the dispersive power of prism can be represented as:

${\mathrm{n}}_{\mathrm{v}}=\frac{{\mathrm{n}}_{\mathrm{v}}-{\mathrm{n}}_{\mathrm{G}}}{\mathrm{n}}$

and,

${\mathrm{n}}_{\mathrm{v}}=\frac{\sin \left({\displaystyle \frac{\mathrm{A}+{\mathrm{D}}_{\mathrm{v}}}{2}}\right)}{\sin {\displaystyle \frac{\mathrm{A}}{2}}}$

${\mathrm{n}}_{\mathrm{G}}=\frac{\sin \left({\displaystyle \frac{\mathrm{A}+{\mathrm{D}}_{\mathrm{G}}}{2}}\right)}{\sin {\displaystyle \frac{\mathrm{A}}{2}}}$

$\mathrm{n}=\frac{{\mathrm{n}}_{\mathrm{v}}}{{\mathrm{n}}_{\mathrm{G}}}$

Here,

D is the angle of minimum deviation.

‘n’ is the refractive index of the material of the prism.

Therefore, the prism's dispersive power can sometimes be described from the perspective of the angle constructed from two maximal wavelengths.