Question

The refractive indices of flint glass for red and violet lights are $1.613$ and $1.632$ respectively. Find the angular dispersion produced by a thin prism of flint glass having refracting angle $5^{\circ }$.

• A. ${0.05}^{\circ }$
• B. ${0.072}^{\circ }$
• C. ${0.095}^{\circ }$
• D. ${0.32}^{\circ }$

Answer 1

The correct option is C ${0.095}^{\circ }$

Given,

${\mu }_r=1.613;{\mu }_v=1.632;A=5^{\circ }$

Deviation of the red light is given by,

${\delta }_r=({\mu }_r-1)A$

Deviation of the violet light is given by,

${\delta }_v=({\mu }_v-1)A$

The angular dispersion $\left(\theta \right)$ is given by,

$\theta ={\delta }_v-{\delta }_r=({\mu }_v-1)A-({\mu }_r-1)A$

$=({\mu }_v-{\mu }_r)A=(1.632-1.613)\times 5^{\circ }$

$\therefore \theta ={0.095}^{\circ }$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.

Why this question ? Note: Deviation of beam (also called mean deviation) $\delta ={\delta }_y=({\mu }_y-1)A$ ${\mu }_v,{\mu }_r$ and ${\mu }_y$ are $R.I.$ of material for violet, red and yellow colours respectively. Numerical data reveals that if the average value of $\mu$ is small, ${\mu }_v-{\mu }_r$ is also small and if the average value of $\mu$ is large ${\mu }_v-{\mu }_r$ is also large. Thus, the larger the mean deviation, the larger will be the angular dispersion.