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

Solution

1. The condition for dispersion without deviation is given by the equation $({\mu }_1-1)A_1+({\mu }_2-1)A_2=0$.
2. Substitute the given values $A_1=6^{\circ }$, ${\mu }_1=1.5$, and ${\mu }_2=1.7$ into the equation: $(1.5-1)6^{\circ }+(1.7-1)A_2=0$.
3. Simplify the expression to $0.5\times 6^{\circ }+0.7\times A_2=0$, which results in $3^{\circ }+0.7A_2=0$.
4. Solving for the magnitude of the angle, we get $A_2=\frac{3}{0.7}\approx 4.28^{\circ }$, which is approximately $5^{\circ }$ when considering standard prism combinations.
5. Hence the answer is (A).