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 ${\mu }_2=1.6$
$\therefore A=A_2=9\times \frac{(1.4-1)}{(1.6-1)}$
$=9\times \frac{0.4}{0.6}=6^{\circ }$