Question

A ray of light passes through a prism whose refracting angle is 5${}^o$ and dispersive power is 0.03. The refractive index for the mean ray in a spectrum is 1.62. The mean deviation and angle of dispersion respectively are

• A. ${3.1}^o,{0.077}^o$
• B. ${3.1}^o,{0.093}^o$
• C. ${6.2}^o,0.093$
• D. ${6.2}^o,{0.077}^o$

Answer 1

Answer: (B)

${3.1}^o,{0.093}^o$

DISPERSION OF LIGHT:

For a thin prism with apex angle $A$ and refractive index $\mu$, the deviation produced is 

$d=(\mu -1)A$

The ratio of angular dispersion for two extreme&nbsp;colours to their mean deviation is called&nbsp;<span>dispersive power of prism ( $\omega$ ) Dispersive power $=$ ( $\omega$ ) $=$ $\frac{Angulardispersion}{meandeviation}$.

Dispersive power does not depend upon the angle&nbsp;of prism. It only depends upon material.

Mean deviation is given by

$d=(\mu -1)A=(1.62-1)5={3.1}^{\circ }$

Using formula for dispersive power we can find angle of dispersion:

$Dispersivepower=\frac{Angulardispersion}{Meandeviation}$

$0.03=\frac{\varphi }{3.1}$

$\varphi =3.1\times 0.03=0.093$.