A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are $1.620$ and $1.518$, respectively. If the refracting angle of the flint prism is $6.0°$, what would be the refracting angle of the crown prism?

Three thin prisms are combined as shown in the figure. The refractive indices of the crown glass for red, yellow and violet rays are ${\mathit{\mu }}_{\mathit{r}},\mathit{ }{\mathit{\mu }}_{\mathit{y}}$ and ${\mathit{\mu }}_{\mathit{v}}$ respectively and those for the flint glass are ${{\mathit{\mu }}_{\mathit{r}}}^{\mathit{\text{'}}}\mathit{,}\mathit{ }{{\mathit{\mu }}_{\mathit{y}}}^{\text{'}}$and ${{\mu }_{\mathit{v}}}^{\text{'}}$ respectively. Find the ratio $\frac{A^{\text{'}}}{A}$ for which (a) system produces deviation without dispersion(achromatic combination)and (b) system produces dispersion without deviation(direct vision arrangement). 

A thin prism of angle $6.0°$, $\omega =0.07$ and ${\mu }_y=1.50$ is combined with another thin prism having $\omega =0.08$ and ${\mu }_y=1.60$. The combination produces no deviation in the mean ray.

$\left(\mathrm{a}\right)$ Find the angle of the second prism.

$\left(\mathrm{b}\right)$ Find the net angular dispersion produced by the combination when a beam of white light passes through it.

$\left(\mathrm{c}\right)$ If the prisms are similarly directed, what will be the deviation in the mean ray?

$\left(\mathrm{d}\right)$ Find the angular dispersion in the situation described in $\left(\mathrm{c}\right)$.

Two mirrors are inclined at an angle $\mathrm{\theta }$ as shown in the figure. Light ray is incident parallel to one of the mirrors. Light will start retracing its path after third reflection if: