Lens problem with another medium of refractive index =2

[Sumedh]

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

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Homework Statement

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

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.

 

[jbsteele]

Solution:Using the lens maker's formula, we can find the new focal length.F = (n-1)*R2/(n*(R1-R2))where n is the refractive index of the medium and R1 and R2 are the radii of curvature of the two surfaces.In this case, n = 2, R1 = ∞, and R2 = 20 cm. Therefore, the new focal length is F = (2-1)(20 cm)/(2*(∞ - 20 cm)) = 40 cm.