Question

In the visible region, the dispersive powers and the mean angular deviations for crown and flint glass prisms are $\omega$ and ${\omega }^{{}^{\prime }}$ and d and $d^{{}^{\prime }}$ respectively. When the two prism are combined, the condition of zero dispersion by the combination is

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

Answer 1

The correct option is A $\sqrt{\omega d}+\sqrt{{\omega }^{{}^{\prime }}{d}^{{}^{\prime }}}=0$

${\theta }_{net}=\theta +{\theta }^{\prime }=0\Rightarrow \omega d+{\omega }^{\prime }{d}^{\prime }=0$
($\theta =$ Angular dispersion $=\omega .{\delta }_y$)