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. Find the angle of the second prism $A_2$.

Solution

1. The condition for zero net deviation is $({\mu }_1-1)A_1+({\mu }_2-1)A_2=0$.
2. Substitute the given values: $(1.5-1)6+(1.7-1)A_2=0$.
3. This simplifies to $0.5\times 6+0.7\times A_2=0$.
4. Solving for $A_2$ gives $A_2=-3/0.7\approx -4.28$, but assuming standard prism combination logic for magnitude, hence the answer is (A).