Question

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

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

Answer 1

The correct option is C $3^{\circ }$

Net deviation due to to two prisms is zero

$\therefore {\delta }_1+{\delta }_2=0$

$A_1({\mu }_1-1)+A_2({\mu }_2-1)=0\delta =A(\mu -1$
Here $A_1,{\mu }_1\text{and}{\delta }_1$ are for prism $P_1$

$A_2,{\mu }_2\text{and}{\delta }_2$ are for prism $P_2$

$\therefore A_2=\frac{-A_1({\mu }_1-1)}{({\mu }_2-1)}=\frac{-4^{\circ }(1.54-1)}{(1.72-1)}$

$A_2=\frac{-4^{\circ }\times 0.54}{0.72}$

$A_2=-3^{\circ }$

The two prisms are combined such that the position of one prism is inverted with respect to other prism.