Question

A thin prism with angle of prism $A={10}^{\circ }$ has refractive index of $1.627$ for red light and $1.648$ for violet light. The angular dispersion produced by the prism will be :

• A. ${0.37}^{\circ }$
• B. ${0.0021}^{\circ }$
• C. ${0.021}^{\circ }$
• D. ${0.21}^{\circ }$

Answer 1

The correct option is D ${0.21}^{\circ }$

Given :
Refracting angle is $\left(A\right)={10}^{\circ }$

Refractive index for red light is $\left({\mu }_R\right)=1.627$

Refractive index for violet light is $\left({\mu }_V\right)=1.648$

Deviation of a light ray inside a thin prism is given by :
$\delta =(\mu -1)A$

Therefore,
Angular dispersion $={\delta }_V-{\delta }_R$​

$=({\mu }_V-{\mu }_R)A$

$=(1.648-1.627)10$

$=\left(0.021\right)\times 10$

$={0.210}^{\circ }$

Hence, option $\left(a\right)$ is the correct answer.