Question

A thin glass prism of angle $9^{\circ}$ with refractive index $1.4$ is combined with another glass prism of refractive index $1.6$, as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle $(A)$ o $f$ the second prism.

• A. $9^{\circ}$
• B. $12^{\circ}$
• C. $6^{\circ}$
• D. $4^{\circ}$

Answer 1

Answer: (C)

For dispersion without deviation through a prism combination,
$\delta_{m_{1}}=\delta_{m_{2}}$
$\Rightarrow A_{1}\left(\mu_{1}-1\right)=A_{2}\left(\mu_{2}-1\right)$
$\Rightarrow A_{2}=A_{1} \frac{\left(\mu_{1}-1\right)}{\left(\mu_{2}-1\right)}$
Here, $A_{1}=9^{\circ}, \mu_{1}=1.4$ and $\mu_{2}=1.6$
$\therefore A=A_{2}=9 \times \frac{(1.4-1)}{(1.6-1)}$
$=9 \times \frac{0.4}{0.6}=6^{\circ}$