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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 $(A)$ of the second prism.
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The correct answer is:
$6^{\circ}$
For dispersion without deviation through a prism combination,
$\delta_{m_1}=\delta_{m_2} \Rightarrow A_1\left(\mu_1-1\right)=A_2\left(\mu_2-1\right)$
Here, $A_1=9^{\circ}, \mu_1=1.4$ and $\mu_2=1.6$
$\therefore \quad A=A_2=9 \times \frac{(1.4-1)}{(1.6-1)}=9 \times \frac{0.4}{0.6}=6^{\circ}$
$\delta_{m_1}=\delta_{m_2} \Rightarrow A_1\left(\mu_1-1\right)=A_2\left(\mu_2-1\right)$
Here, $A_1=9^{\circ}, \mu_1=1.4$ and $\mu_2=1.6$
$\therefore \quad A=A_2=9 \times \frac{(1.4-1)}{(1.6-1)}=9 \times \frac{0.4}{0.6}=6^{\circ}$
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