A thin lens made of glass (refractive index <math> <mo>=</mo> <mn>1.5</mn> </math> ) of focal length <math> <mi>f</mi> <mo>=</mo> <mn>16</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> is immersed in a liquid of refractive index 1.42. If its focal length in liquid is <math> <msub> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </math> , then the ratio <math> <msub> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </math> /f is closest to the integer:

1 f = μ g - 1 1 R 1 - 1 R 2 <!- [endif]-><!- [endif]-> 1 f l = μ g μ l - 1 1 R 1 - 1 R 2 <!- [endif]-><!- [endif]-> (i) f l f = μ g - 1 μ g μ l - 1 = 1.5 - 1 1.5 1.41 - 1 = 8.875 ≈ 9 .

A thin lens made of glass (refractive index <math> <mo>=</mo> <mn>1.5</mn> </math> ) of focal length <math> <mi>f</mi> <mo>=</mo> <mn>16</mn> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> is immersed in a liquid of refractive index 1.42. If its focal length in liquid is <math> <msub> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </math> , then the ratio <math> <msub> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </math> &nbsp;/f is closest to the integer: &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics Class 12th Physics Ray Optics and Optical Instruments

A thin lens made of glass (refractive index $= 1.5$ ) of focal length $f = 16 c m$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{l}$ , then the ratio $f_{l}$ /f is closest to the integer:

Option 1 -

Option 2 -

Option 3 -

Option 4 -

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

$\frac{1}{f} = (μ_{g} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f_{l}} = (\frac{μ_{g}}{μ_{l}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

(i) $\frac{f_{l}}{f} = \frac{μ_{g} - 1}{\frac{μ_{g}}{μ_{l}} - 1} = \frac{1.5 - 1}{\frac{1.5}{1.41} - 1} = 8.875 \approx 9$ .

<math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mi>f</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfenced separators="|"> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mi>g</mi> </mrow> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </mfenced> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> <!- [endif]-><!- [endif]-> <math> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </mfenced> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">R</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> <!- [endif]-><!- [endif]-> (i) <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> <mo>-</mo> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="script">l</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1.5</mn> <mo>-</mo> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>1.5</mn> </mrow> </mrow> <mrow> <mrow> <mn>1.41</mn> </mrow> </mrow> </mfrac> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>8.875</mn> <mo>≈</mo> <mn>9</mn> </math> .

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A thin lens made of glass (refractive index $= 1.5$ ) of focal length $f = 16 c m$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{l}$ , then the ratio $f_{l}$ /f is closest to the integer:

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A thin lens made of glass (refractive index = 1.5 ) of focal length f = 16 c m is immersed in a liquid of refractive index 1.42. If its focal length in liquid is f l , then the ratio f l /f is closest to the integer:

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A thin lens made of glass (refractive index $= 1.5$ ) of focal length $f = 16 c m$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{l}$ , then the ratio $f_{l}$ /f is closest to the integer: