A thin prism of angle $A_1=6^{\circ }$ and refractive index ${\mu }_1=1.5$ is combined with another thin prism of refractive index ${\mu }_2=1.7$ to produce dispersion without deviation. What is the angle $A_2$ of the second prism?

Solution

1. The condition for deviation without dispersion (or in this case, zero net deviation) for two thin prisms is given by $A_1({\mu }_1-1)+A_2({\mu }_2-1)=0$.
2. Substituting the given values $A_1=6^{\circ }$, ${\mu }_1=1.5$, and ${\mu }_2=1.7$, we use the magnitude relation $A_1({\mu }_1-1)=A_2({\mu }_2-1)$.
3. Plugging in the values gives $6(1.5-1)=A_2(1.7-1)$, which simplifies to $6(0.5)=A_2(0.7)$.
4. Solving for $A_2$ yields $A_2=3/0.6$, which results in $A_2=5^{\circ }$.
5. Hence the answer is (A).