Refraction at Curved Surface Formulas
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Complete Refraction at Curved Surface Formulae
\(\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}\)
If right sign convention is taken this formula is valid for all types of cases.
1. Lateral magnification
m = \(\frac{h_{i}}{h_{o}}=\frac{v}{u}\)
2. Lens formula
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)3. Lens makerΓÇÖs formula
\(\frac{1}{f}=\left(\mu_{r e l}-1\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right], \mu_{r e l}=\frac{\mu_{2}}{\mu_{1}}\)
when both sides of lens have different media.
\(\frac{\mu_{3}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R_{1}}+\frac{\mu_{3}-\mu_{2}}{R_{2}}\)
4. Power of lens
f → focal length of lens in air P = \(\frac{\mu}{f}\)
µ → refractive index of medium in which the lens is placed. If f is in meter then P is in diopter.
5. Combination of Lenses
(i) \(\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}+\ldots \ldots+\frac{1}{f_{n}}\)
P = P1 + P2 ……… Pn
(ii) when lenses are separated at a distance ‘d’
\(\frac{1}{f_{e q}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{d}{f_{1} f_{2}}\)
or P = P1 + P2 – dP1P2
6. Lens with one surface silvered
P = PL + Pm + PL = 2PL + Pm
PL → power of lens
Pm → power of mirror
\(\frac{1}{f_{e q}}=\frac{2}{f_{L}}+\frac{1}{f_{m}}\left(\begin{array}{c}
P_{m}=-\frac{1}{f_{m}} \\
f_{m}=\frac{R_{m}}{2}
\end{array}\right)\)
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