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A thin lens made of a material of refrac...

A thin lens made of a material of refractive index `mu_(0)` has a focal length `f_(0)` in air. Find the focal length of this lens if it is immersed in a liquid of refractive index `mu`.

Text Solution

Verified by Experts

From lensmaker's formula, we know that
`(1)/(f_(0))=(mu_(0)-1)((1)/(R_(1))-(1)/(R_(2)))` (i)
When the lens is immersed in a liquid of refractive index `mu`, then
`(1)/(f)=((mu_(0))/(mu)-1)((1)/(R_(1))-(1)/(R_(2)))` (ii)
From Eqs. (i) and (ii), we get
`(1)/(f)=((mu_(0)=mu)1)/(mu(mu_(0)-1)f_(0))`
or `f=f_(0)[(mu(mu_(0)-1))/(mu_(0)-mu)]`
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