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.