Question
The minimum deviations suffered by red, 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.
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Answer
Given that, $\delta_\text{r}=38.4^\circ,\delta_\text{y}=38.7^\circ\ \text{and}\ \delta_\text{v}=39.2^\circ$
Dispersive power $=\frac{\mu_\text{v}-\mu_\text{r}}{\mu_\text{y}-1}=\frac{(\mu_\text{v}-1)-(\mu_\text{r}-1)}{(\mu_\text{y}-1)}$ $=\frac{\Big(\frac{\delta_\text{v}}{\text{A}}\Big)-\Big(\frac{\delta_\text{r}}{\text{A}}\Big)}{\Big(\frac{\delta_\text{v}}{\text{A}}\Big)}\ [\because\delta=(\mu-1)\text{A}]$
$=\frac{\delta_\text{v}-\delta_\text{r}}{\delta_\text{y}}=\frac{39.2-3.84^\circ}{38.7}=0.0204$
Dispersive power $=\frac{\mu_\text{v}-\mu_\text{r}}{\mu_\text{y}-1}=\frac{(\mu_\text{v}-1)-(\mu_\text{r}-1)}{(\mu_\text{y}-1)}$ $=\frac{\Big(\frac{\delta_\text{v}}{\text{A}}\Big)-\Big(\frac{\delta_\text{r}}{\text{A}}\Big)}{\Big(\frac{\delta_\text{v}}{\text{A}}\Big)}\ [\because\delta=(\mu-1)\text{A}]$
$=\frac{\delta_\text{v}-\delta_\text{r}}{\delta_\text{y}}=\frac{39.2-3.84^\circ}{38.7}=0.0204$
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