Question

In the visible region the dispersive powers and the mean angular deviations for crown glass and flint glass prism are $\omega ,{\omega }^1$ and $d,d^1$ respectively. The condition for getting dispersion with zero deviation when the two prisms are combined is

• A. $\sqrt{\omega d}+\sqrt{{\omega }^1{d}^1}=0$
• B. ${\omega }^{1}d+\omega d^1$=0
• C. $\omega d+{\omega }^1{d}^1$=0
• D. $\omega d^2+({\omega }^1{d}^1{)}^2$=0

Answer 1

The correct option is C $\omega d+{\omega }^1{d}^1$=0

Given: dispersive power $\omega ,{\omega }^{{}^{\prime }}$
Mean deviation: $d,d^{{}^{\prime }}$
Dispersive power $\omega$ $=\frac{\text{angular disperion}}{\text{mean deviation}}$

$\Rightarrow$ Angular dispersion $=$ Dispersive power $\times$ mean deviation
So, $\omega d+{\omega }^{{}^{\prime }}{d}^{{}^{\prime }}=0$ for getting dispersion with zero deviation.