# JEE Main & Advanced Physics Ray Optics Lens Immersed in a Liquid

Lens Immersed in a Liquid

Category : JEE Main & Advanced

If a lens (made of glass) of refractive index ${{\mu }_{g}}$ is immersed in a liquid of refractive index ${{\mu }_{l}}$, then its focal length in liquid, ${{f}_{l}}$ is given by        $\frac{1}{{{f}_{l}}}=({{\,}_{l}}{{\mu }_{g}}-1)\,\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)$                    ......(i)

If ${{f}_{a}}$ is the focal length of lens in air, then

$\frac{1}{{{f}_{a}}}=({{\,}_{a}}{{\mu }_{g}}-1)\,\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)$                 ......(ii)

$\Rightarrow$$\frac{{{f}_{l}}}{{{f}_{a}}}=\frac{{{(}_{a}}{{\mu }_{g}}-1)}{{{(}_{l}}{{\mu }_{g}}-1)}$ (1) If ${{\mu }_{g}}>{{\mu }_{l}},$ then ${{f}_{l}}$ and ${{f}_{a}}$ are of same sign and ${{f}_{l}}>{{f}_{a}}$.

That is the nature of lens remains unchanged, but it's focal length increases and hence power of lens decreases.

(2) If ${{\mu }_{g}}={{\mu }_{l}},$ then ${{f}_{l}}=\infty$. It means lens behaves as a plane glass plate and becomes invisible in the medium.

(3) If ${{\mu }_{g}}<{{\mu }_{l}},$ then ${{f}_{l}}$ and ${{f}_{a}}$ have opposite signs and the nature of lens changes i.e. a convex lens diverges the light rays and concave lens converges the light rays.

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