Question

A thin prism $R_{1}$ of angle $4^{\circ}$ and refractive index $1.54^{\circ}$ is combined with another thin prism $P_{2}$ of refractive index $1.72$ to produce dispersion without deviation. The angle of $P_{2}$ is

• A. $4^{\circ}$
• B. $5.33^{\circ}$
• C. $2.6^{\circ}$
• D. $3^{\circ}$

Answer 1

Answer: (D)

$3^{\circ}$

Answer 2

Angle of deviation $\delta=(n-1) A$. Dispersion produced by both the prism's will be equal. $\left(n_{1}-1\right) A_{1}=\left(n_{2}-1\right) A_{2}$ $\Rightarrow A_{2}= \frac{\left(n_{1}-1\right) A_{1}}{\left(n_{2}-1\right)}$ $=\frac{(1.54-1)}{(1.72-1)}=3^{\circ}$ Hence, the angle of prism $P_{2}$ is $3^{\circ}$