Question

In an achromatic combination of two prisms made of materials with dispersive powers $0.2$ and $0.25$, if the angular dispersion produced by each prism is $100$, the net deviation is:

• A. ${10}^{\circ }$
• B. $1^{\circ }$
• C. $5^{\circ }$
• D. ${2.5}^{\circ }$

Answer 1

The correct option is A ${10}^{\circ }$

We know that dispersive power of a prism is given by:

$\omega =\frac{\theta }{{\delta }_Y}$,

${\delta }_Y=\frac{\theta }{\omega }$,

Given: $\omega =0.2,{\omega }^{\prime }=0.25,\theta ={\theta }^{\prime }={10}^o$,

Therefore, net deviation is:

${\delta }_Y-{\delta }_Y^{\prime }=\frac{\theta }{\omega }-\frac{{\theta }^{\prime }}{{\omega }^{\prime }}$,

${\delta }_Y-{\delta }_Y^{\prime }=\frac{10}{0.2}-\frac{10}{0.25}={10}^o$