Ray Optics

JEE Main level, single correct, medium

182 of 295

Question 182 of 295

Curved surfaces of a plano-convex lens of refractive index μ1{\mu }_{1} and a plano-concave lens of refractive index μ2{\mu }_{2} have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses

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Answer: (D) μ1−μ2{\mu }_{1}-{\mu }_{2}

1f1=(μ1−1)[1R]\dfrac{1}{{f}_{1}}=\left({\mu }_{1}-1\right)\left[\dfrac{1}{R}\right]
1f2=(μ2−1)[1−R]⇒1feq=1f1+1f2=(μ1−1)R−(μ2−1)R\dfrac{1}{{f}_{2}}=\left({\mu }_{2}-1\right)\left[\dfrac{1}{-R}\right]\Rightarrow \dfrac{1}{{f}_{eq}}=\dfrac{1}{{f}_{1}}+\dfrac{1}{{f}_{2}}=\dfrac{\left({\mu }_{1}-1\right)}{R}-\dfrac{\left({\mu }_{2}-1\right)}{R}
1feq=(μ1−μ2)R⇒Rfeq=μ1−μ2\dfrac{1}{{f}_{eq}}=\dfrac{\left({\mu }_{1}-{\mu }_{2}\right)}{R}\Rightarrow \dfrac{R}{{f}_{eq}}={\mu }_{1}-{\mu }_{2}

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