# JEE Main & Advanced Physics Ray Optics Lens Maker's Formula and Lens Formula

Lens Maker's Formula and Lens Formula

Category : JEE Main & Advanced

(1) Lens maker's formula : If ${{R}_{1}}$ and ${{R}_{2}}$ are the radii of curvature of first and second refracting surfaces of a thin lens of focal length f and refractive index $\mu$ (w.r.t. surrounding medium) then the relation between f, m, ${{R}_{1}}$ and ${{R}_{2}}$ is known as lens maker's formula.

$\frac{1}{f}=(\mu -1)\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)$

Focal length of different lenses

 Lens Focal length For  $\mu =1.5$ Biconvex lens ${{R}_{1}}=R$ ${{R}_{2}}=-R$ $f=\frac{R}{2(\mu -1)}$ $f=R$ Plano-convex lens ${{R}_{1}}=\infty$ ${{R}_{2}}=-R$ $f=\frac{R}{(\mu -1)}$ $f=2R$ Biconcave ${{R}_{1}}=-R$ ${{R}_{2}}=+R$ $f=-\frac{R}{2(\mu -1)}$ $f=-R$ Plano-concave ${{R}_{1}}=\infty$ ${{R}_{2}}=R$ $f=\frac{-R}{(\mu -1)}$ $f=-2R$

(2) Lens formula : The expression which shows the relation between u, v and f is called lens formula.

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

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