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 prisms produces dispersion without deviation. The angle of the second prism should be

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

Answer 1

Answer: (C)

Deviation = zero
So, $\delta ={\delta }_1+{\delta }_2=0$
$\Rightarrow \left({\mu }_1-1\right)A_1+\left({\mu }_2-1\right)A_2=0$
$\Rightarrow A_2(1.75-1)=-(1.5-1)15^{\circ }$
$\Rightarrow A_2=-\frac{0.5}{0.75}\times 15^{\circ }$
or $A_2=-10^{\circ }.$
Negative sign shows that the second prism is inverted with respect to the first.