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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