Question

A thin prism $P_1$ with angle $4^o$ and made from glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. What is the angle of the prism $P_2$?

• A. $3^o$
• B. $6^o$
• C. $9^o$
• D. ${12}^o$

Answer 1

The correct option is A $3^o$

In case of thin prism $\delta =(\mu -1)A$, when two prisms are combined together,
$\delta ={\delta }_1+{\delta }_2=(\mu -1)A+({\mu }^{\prime }-1)A^{\prime }$
For producing dispersion without deviation
$\delta =0$ i.e., $({\mu }^{\prime }-1)A^{\prime }=-(\mu -1)A$
or $A^{\prime }=\frac{(1.54-1)}{(1.72-1)}\times 4^o=-3^o$
So the angle of the other prism is $3^o$ and opposite to the first.