Question

used these expression to derived lens maker formula.draw the necessary diagram

Answer 1

hello friend...!!

DERIVATION OF LENS MAKER FORMULA :

• From rarer to denser the refraction of light through a spherical surface is,


$\frac{ \gamma 1}{ - u} + \frac{ \gamma 2}{v2} = \frac{ \gamma 2 - \gamma 1}{r1}$

similarly, from denser to rarer the refraction of light through a spherical surface is,

$\frac{ \gamma 2}{ - v2} + \frac{ \gamma 1}{v} = \frac{ \gamma 1 - \gamma 2}{r2}$


now, by adding the above equations we get ,

$\frac{ \gamma 1}{ - u} + \frac{ \gamma 2}{v2} - \frac{ \gamma 2}{2} + \frac{ \gamma 1}{v} = \frac{ \gamma 2 - \gamma 1}{r1} + \frac{ \gamma 1 - \gamma 2}{r2}$
implies,

$\gamma 1( \frac{1}{v} - \frac{1}{u} ) = ( \gamma 2 - \gamma 1)( \frac{1}{r1} - \frac{1}{r2} )$
therefore,

$\gamma 1( \frac{1}{f} ) = ( \gamma 2 - \gamma 1)( \frac{1}{r1} - \frac{1}{r2} )$

implies,

$\frac{1}{f} = ( \frac{ \gamma 2 - \gamma 1}{ \gamma 1} )( \frac{1}{r1} - \frac{1}{r2} )$
implies,

$\frac{1}{f} = ( \frac{ \gamma 2}{ \gamma 1} - 1)( \frac{1}{r1} - \frac{1}{r2} )$
therefore the lens maker formula is,

$\frac{1}{f } = ( \gamma - 1)( \frac{1}{r1} - \frac{1}{r2} )$

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the attached picture gives you the ray diagram

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hope it helps...!!