Question

A thin prism $P_1$ with angle $4{}^{\circ }$ and made from glass of refractive index $1.54$ is combined with another prism $P_2$ made of glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is

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

Answer 1

Answer: (D)

For a thin prism, angle of minimum deviation is given by $\delta =(\mu -1)A$
where, $\mu$ is refractive index of the prism and $A$ the angle of prism.
For dispersion without deviation
${\delta }_1={\delta }_2$
$\Rightarrow \left({\mu }_1-1\right)A_1=\left({\mu }_2-1\right)A_2$
$\Rightarrow A_2=\frac{\left({\mu }_1-1\right)}{\left({\mu }_2-1\right)}{A}_1$
Given, ${\mu }_1=1.54,A_1=4^{\circ },{\mu }_2=1.72$
$\Rightarrow A_2=\frac{(1.54-1)}{(1.72-1)}\times 4=3^{\circ }$