Question

A thin prism $P_{1}$ with angle $6^{\circ}$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_{2}$ of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_{2}$ will be

• A. $4^{\circ} 30' $
• B. $ 8.5^{\circ} $
• C. $ 6.5^{\circ} $
• D. None of these

Answer 1

Answer: (A)

For dispersion without deviation
$\delta_{1}+\delta_{2}=0$
where $\delta_{1}=\mu-1 A_{1}, \delta_{2}=\left(\mu_{2}-1\right) A_{2}$
$A_{2}=-\frac{\left(\mu_{1}-1\right)}{\left(\mu_{2}-1\right)} \times A$
Given, $\mu_{1}=1.54, \mu_{2}=1.72, A_{1}=6^{\circ}$
$A_{2}=-\frac{(1.54-1)}{(1.72-1)} \times 6^{\circ}$
$A_{2} =-\frac{0.54}{0.72} \times 6^{\circ}$
$=-\frac{3}{4} \times 6^{\circ}=-4.50^{\circ} $
$\Rightarrow A_{2} =4^{\circ} 30'$