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. $4^{\circ }30^{\prime }$
• 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 ${\delta }_1=\mu -1A_1,{\delta }_2=\left({\mu }_2-1\right)A_2$
$A_2=-\frac{\left({\mu }_1-1\right)}{\left({\mu }_2-1\right)}\times A$
Given, ${\mu }_1=1.54,{\mu }_2=1.72,A_1=6^{\circ }$
$A_2=-\frac{(1.54-1)}{(1.72-1)}\times 6^{\circ }$
$A_2=-\frac{0.54}{0.72}\times 6^{\circ }$
$=-\frac{3}{4}\times 6^{\circ }=-4.50^{\circ }$
$\Rightarrow A_2=4^{\circ }30^{\prime }$