A thin prism of angle $6.0^\circ,\omega=0.07$ and $\mu_\text{y}=1.50$ is combined with another thin prism having $\omega=0.08$ and $\mu_\text{y}=1.60.$ The combination produces no deviation in the mean ray.
- Find the angle of the second prism.
- Find the net angular dispersion produced by the combination when a beam of white light passes through it.
- If the prisms are similarly directed, what will be the deviation in the mean ray
- Find the angular dispersion in the situation described in (c).
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Given that, $\text{A}'=6^\circ,\ \omega'=0.07,\ \mu'_\text{y}=1.50$
$\text{A}=?\ \omega=0.08,\ \mu_\text{y}=1.60$
The combination produces no deviation in the mean ray.
$\Rightarrow(1.60-1)\text{A}=(1.50-1)\text{A}'$
$\Rightarrow\text{A}=\frac{0.50\times6^\circ}{0.60}=5^\circ$
$\Rightarrow(1.60-1)(0.08)(5^\circ)-(1.50-1)(0.07)(6^\circ)$
$\Rightarrow0.24^\circ-0.21^\circ=0.03^\circ$
$\delta_\text{y}=(\mu_\text{y}-1)\text{A}+(\mu'_\text{y}-1)\text{A}$
$=(1.60-1)5^\circ+(1.50-1)6^\circ=3^\circ+3^\circ=6^\circ$
$\text{A}=?\ \omega=0.08,\ \mu_\text{y}=1.60$
The combination produces no deviation in the mean ray.
- $\delta_\text{y}=(\mu_\text{y}-1)\text{A}-(\mu'_\text{y}-1)\text{A}'=0$ [Prism must be oppositely directed]
$\Rightarrow(1.60-1)\text{A}=(1.50-1)\text{A}'$
$\Rightarrow\text{A}=\frac{0.50\times6^\circ}{0.60}=5^\circ$
- When a beam of white light passes through it,
$\Rightarrow(1.60-1)(0.08)(5^\circ)-(1.50-1)(0.07)(6^\circ)$
$\Rightarrow0.24^\circ-0.21^\circ=0.03^\circ$
- If the prisms are similarly directed,
$\delta_\text{y}=(\mu_\text{y}-1)\text{A}+(\mu'_\text{y}-1)\text{A}$
$=(1.60-1)5^\circ+(1.50-1)6^\circ=3^\circ+3^\circ=6^\circ$
- Similarly, if the prisms are similarly directed, the net angular dispersion is given by,
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