Ray Optics

JEE Main level, single correct, medium

206 of 295

Question 206 of 295

A thin convex lens made from crown glass (μ=32)\left(\mu =\dfrac{3}{2}\right) has focal length f⁡f⁡. When it is measured in two different liquids having refractive indices 43\dfrac{4}{3} and 53\dfrac{5}{3}, it has the focal lengths f⁡1{f⁡}_{1} and f⁡2{f⁡}_{2} respectively. The correct relation between the focal lengths is :

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Answer: (B) f⁡1>f⁡{f⁡}_{1}\gt f⁡ and f⁡2{f⁡}_{2} becomes negative

Let[1R1−1R2]=x\text{Let} [\dfrac{1}{{\text{R}}_{1}}-\dfrac{1}{{\text{R}}_{2}}]=\text{x}

∴1f=[321−1][1R1−1R2]⇒f=2x∴ \dfrac{1}{\text{f}}=[\dfrac{\dfrac{3}{2}}{1}-1][\dfrac{1}{{\text{R}}_{1}}-\dfrac{1}{{\text{R}}_{2}}] \Rightarrow \text{f}=\dfrac{2}{\text{x}}

When in liquid 1

1f1=[3243−1][1R1−1R2]⇒f1=8x\dfrac{1}{{\text{f}}_{1}}=[\dfrac{\dfrac{3}{2}}{\dfrac{4}{3}}-1][\dfrac{1}{{\text{R}}_{1}}-\dfrac{1}{{\text{R}}_{2}}] \Rightarrow {\text{f}}_{1}=\dfrac{8}{\text{x}}

When in liquid 2

1f2=[3253−1][1R1−1R2]⇒f2=−10x\dfrac{1}{{\text{f}}_{2}}=[\dfrac{\dfrac{3}{2}}{\dfrac{5}{3}}-1][\dfrac{1}{{\text{R}}_{1}}-\dfrac{1}{{\text{R}}_{2}}] \Rightarrow {\text{f}}_{2}=\dfrac{-\text{10}}{\text{x}}

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