A thin prism of angle 6° and refractive index for yellow light (nY)… | JEE Main 2022 (27 Jul, Shift 2)

Q54JEE Main 2022 · 27 JUL · SHIFT 2Medium

Prism, Dispersion & Scattering

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 $n_Y = 1.55$ . The combination produces no dispersion. The net average deviation $(\delta)$ produced by the combination is $\left(\frac{1}{x}\right)^\circ$ . The value of $x$ is ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

The prisms are inverted relative to each other, so their deviations subtract.
$\delta = (n_1 - 1)A_1 - (n_2 - 1)A_2$
$\delta = 0.5 \times 6^\circ - 0.55 \times 5^\circ = 3^\circ - 2.75^\circ = 0.25^\circ$
$\delta = \left(\tfrac{1}{4}\right)^\circ \Rightarrow x = 4$

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