Ray Optics

JEE Main level, single correct, medium

251 of 295

Question 251 of 295

A thin prism P1{P}_{1} with an angle 6∘6^{\circ} and made of glass of refractive index 1.541.54 is combined with another prism P2{P}_{2} made from glass of refractive index 1.721.72 to produce dispersion without average deviation. The angle of prism P2{P}_{2} is :

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Answer: (D) 4.5∘4.5^{\circ}

For no average deviation,
δ1+δ2=0⇒A(μ1−1)−B(μ2−1)=0{\delta }_{1}+{\delta }_{2}=0 \Rightarrow A\left({\mu }_{1}-1\right)-B\left({\mu }_{2}-1\right)=0
⇒6∘(1.54–1)=θ(1.72–1)\Rightarrow 6^{\circ}(1.54–1)=\theta (1.72–1)
⇒θ=6∘×0.540.72\Rightarrow \theta =\dfrac{6^{\circ}\times 0.54}{0.72}
=4.5∘=4.5^{\circ}

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