Question

The minimum deviations suffered by red, yellow and violet beams passing through an equilateral transparent prism are ${38.4}^{\circ },{38.7}^{\circ }$ and ${39.2}^{\circ }$ respectively. Calculate the dispersive power of the medium.

Answer 1

Given that: ${\delta }_1={38.4}^{\circ }$

${\delta }_{ry}={38.7}^{\circ }$ and ${\delta }_y={39.2}^{\circ }$

Dispersive power

$=\frac{{\mu }_y-{\nu }_r}{{\mu }_y-1}$

$=\frac{({\mu }_y-1)-({\mu }_y-1)}{({\mu }_y-1)}$

$=\frac{\frac{\delta }{A}\frac{\delta }{A}}{\frac{{\delta }_r}{A}}[\therefore \delta =(\mu -1\left)A\right]$

$\Rightarrow A=\frac{{\delta }_y-{\delta }_t}{{\delta }_r}=\frac{\left(39.2\right)-\left(38.4\right)}{\left(38.7\right)}$

$=\frac{\left(0.8\right)}{38.70}=0.0204$