# Lens problem with another medium of refractive index =2

1. Oct 10, 2011

### Sumedh

[SOLVED]
I have got the answer.
Answer is 40cm.

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1. The problem statement, all variables and given/known data

Focal length of thin lens in air is 10 cm.now medium of one side of lens is replaced by medium of refractive index μ=2.the radius of curvature of lens with contact with the medium is 20cm. Find the new focal length.
let refractive index of lens=μ
radius of curvature of left surface (R1) of lens is not given
refer attachment

3. The attempt at a solution
assuming parallel rays so u=$\infty$

applying refraction formula at first surface
$μ/v1-1/\infty=μ-1/R1$
similarly

applying refraction formula at second surface
$2/v-μ/v1=2-μ/-20$
adding both

$\frac{μ}{v1}-\frac{1}{\infty}+\frac{2}{v}-\frac{μ}{v1}=\frac{μ-1}{R1}+\frac{2-μ}{-20}$

$\frac{2}{v}=\frac{μ-1}{R1}+\frac{2-μ}{-20}$

After that I am unable to solve
Any help will be highly appreciated.

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Last edited: Oct 10, 2011
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