Q 12-09-149JEE MainJEE Main 2022 (27 Jul, Shift 2)Medium
A thin prism of angle $6^\circ$ and refractive index for yellow light $(n_Y)$ $1.5$ is combined with another prism of angle $5^\circ$ and $n_Y = 1.55$, placed inverted with respect to the first. The combination produces no dispersion. The net average deviation $(\delta)$ produced by the combination is $\left(\dfrac1x\right)^\circ$. The value of $x$ is ______ .
Numerical value type. Enter your answer.
Answer: 4
For a thin prism the deviation of the mean (yellow) ray is $(n_Y - 1)A$. The prisms are inverted relative to each other, so their deviations subtract:
$$\delta = (1.5 - 1)(6^\circ) - (1.55 - 1)(5^\circ) = 3^\circ - 2.75^\circ = 0.25^\circ = \left(\frac14\right)^\circ$$
$x = 4$.
Solution by Sreeraj P, M.Sc Physics