Ray Optics

JEE Main level, numerical answer, medium

252 of 295

Question 252 of 295

A thin prism of angle 6∘6^{\circ} and refractive index for yellow light (nY)1.5\left({n}_{Y}\right)1.5 is combined with another prism of angle 5∘5^{\circ} and nY=1.55{n}_{Y}=1.55. The combination produces no dispersion. The net average deviation (δ)\left(\delta \right) produced by the combination is (1x)∘{\left(\dfrac{1}{x}\right)}^{^{\circ}}. The value of xx is _____ .

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Answer: 4

The formula for deviation due to a thin prism is given by, δ=A(μ−1)\delta =A\left(\mu -1\right).
Therefore, for prism 11:
δ1=6(1.5−1)=3∘{\delta }_{1}=6\left(1.5-1\right)=3^{\circ}
And for prism 22:
δ2=−5(1.55−1)=−2.75∘{\delta }_{2}=-5\left(1.55-1\right)=-2.75^{\circ}
⇒δnet=δ1+δ2=3∘−2.75∘=0.25∘=(14)∘\Rightarrow {\delta }_{net}={\delta }_{1}+{\delta }_{2} =3^{\circ}-2.75^{\circ} =0.25^{\circ} ={\left(\dfrac{1}{4}\right)}^{^{\circ}}
Therefore, x=4x=4.

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