Question

A thin prism of angle ${15}^{\circ }$ made of glass of refractive index ${\mu }_1=1.5$ is combined with another prism of glass of refractive index ${\mu }_2=1.75$. The combination of the prism produces dispersion without deviation. The angle of the second prism should be:

• A. ${12}^{\circ }$
• B. ${10}^{\circ }$
• C. $7^{\circ }$
• D. $5^{\circ }$

Answer 1

The correct option is B ${10}^{\circ }$

Given: $A_1={15}^{\circ }$, ${\mu }_1=1.5$, ${\mu }_2=1.75$, $\delta =0$

We know that
$\delta ={\delta }_1+{\delta }_2$
$\Rightarrow {\delta }_1+{\delta }_2=0$
$\Rightarrow ({\mu }_1-1)A_1+({\mu }_2-1)A_2=0$
$\Rightarrow A_2(1.75-1)=-(1.5-1){15}^{\circ }$
$\Rightarrow A_2=-\frac{0.5}{0.75}\times {15}^{\circ }$

$\therefore A_2=-{10}^{\circ }$

Hence, $\left(B\right)$ is the correct answer.