JEE Main & Advanced Physics Ray Optics Combination of Lens

(1) For a system of lenses, the net power, net focal length and magnification are given as follows :

\[P={{P}_{1}}+{{P}_{2}}+{{P}_{3}}..........\],      \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}+\frac{1}{{{f}_{3}}}+...........\],             

\[m={{m}_{1}}\times {{m}_{2}}\times {{m}_{3}}\times \,............\]

(2) In case when two thin lens are in contact : Combination will behave as a lens, which have more power or lesser focal length.

\[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}\]\[\Rightarrow \]\[F=\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\]     and   \[P={{P}_{1}}+{{P}_{2}}\]

(3) If two lens of equal focal length but of opposite nature are in contact then combination will behave as a plane glass plate and \[{{F}_{\text{combination}}}=\infty \]

(4) When two lenses are placed co-axially at a distance d from each other then equivalent focal length (F).

\[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}-\frac{d}{{{f}_{1}}{{f}_{2}}}\] and \[P={{P}_{1}}+{{P}_{2}}-d{{P}_{1}}{{P}_{2}}\]

(5) Combination of parts of a lens :