Question

The minimum deviations suffered by, yellow and violet beams passing through an equilateral transparent prism are 38.4°, 38.7° and 39.2° respectively. Calculate the dispersive power of the medium.

Answer 1

Given:
Minimum deviations suffered by
Red beam, δ_r = 38.4°
Yellow beam, δ_y = 38.7°
Violet beam, δ_v = 39.2°
If A is the angle of prism having refractive index μ, then the angle of minimum deviation is given by
$\delta =(\mu -1)A$
$\Rightarrow$$\left(\mu -1\right)=\frac{\delta }{A}$ ...(1)
Dispersive power $\left(\omega \right)$ is given by
$$\begin{gathered} \omega =\frac{{\mu }_v-{\mu }_r}{{\mu }_y-1} \\ =\frac{({\mu }_v-1)-({\mu }_r-1)}{({\mu }_y-1)} \end{gathered}$$
From equation (1), we get:
$\omega =\frac{{\displaystyle \frac{{\delta }_v}{A}-\frac{{\delta }_r}{A}}}{{\displaystyle \frac{{\delta }_y}{A}}}$
$\Rightarrow \omega =\frac{{\delta }_v-{\delta }_r}{{\delta }_y}=\frac{(39.2)-(38.4)}{(38.7)}$
$\Rightarrow \omega =\frac{(0.8)}{38.7}=0.0206$
So, the dispersive power of the medium is 0.0206.