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, $\mu_{1}=1.54, A_{1}=4^{\circ}, \mu_{2}=1.72$
$\Rightarrow A_{2}=\frac{(1.54-1)}{(1.72-1)} \times 4=3^{\circ}$