The image of a white object in with light formed by a lens is usually colored and blurred. This defect of image is called chromatic aberration and arises due to the fact that focal length of a lens is different for different colours. As `R` .`I`. `mu` of lens is maximum for violet while minimum for red, violet is focused nearest to the lens while red farthest from it as shown in figure. As a result of this, in case of convergent lens if a screen is placed at `F_(v)` center of the image will be violet and focused while sides are red and blurred. While at `F_(R)` , reverse is the case, `i.e` ., center will be red and focused while sides violet and blurred. The differece between `f_(v)` and `f_(R)` is a measure of the longitudinal chromatic aberration `(L.C.A),i.e.,` `L.C.A.=f_(R)-f_(v)=-df` with `df=f_(v)-f_(R)` ...........`(1)` However, as for a single lens, `(1)/(f)=(mu-1)[(1)/(R_(1))-(1)/(R_(2))]` .............`(2)` `rArr -(df)/(f^(2))=dmu[(1)/(R_(1))-(1)/(R_(2))]` ...............`(3)` Dividing E1n. `(3)` by `(2)` : `-(df)/(f)=(dmu)/((mu-1))=omega, [omega=(dmu)/((mu-1))] "dispersive power" , .........(4)` And hence, from Eqns. `(1)` and `(4)` , `L.C.A.=-df=omegaf` Now, as for a single lens neither `f` nor `omega` zero, we cannot have a single lens free from chromatic aberration. Condition of Achromatism : In case of two thin lenses in contact `(1)/(F)=(1)/(F_(1))+(1)/(F_(2)) i.c,. -(dF)/(F^(2))=(df_(1))/(f_(1)^(2))-(df_(2))/(f_(2)^(2))` The combination will be free from chromatic aberration if `dF=0` `i.e., (df_(1))/(f_(1)^(2))+(df_(2))/(f_(2)^(2))=0` which with the help of Eqn. `(4)` reduces to `(omega_(1)f_(1))/(f_(1)^(2))+(omega_(2)f_(2))/(f_(2)^(2))=0 , i.e., (omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0 ........(5)` This condition is called condition of achromatism (for two thin lenses in contact ) and the lens combination which satisfies this condition is called achromatic lems, from this condition, `i.e.,` form Eqn. `(5)` it is clear the in case of achromatic doublet : Since, if `omega_(1)=omega_(2), (1)/(f_(1))+(1)/(f_(2))=0 i.e., (1)/(F)=0` or `F=infty` `i.e.,` combination will not behave as a lens, but as a plane glass plate. `(2)` As `omega_(1)` and `omega_(2)` are positive quantities, for equation `(5)` to hold, `f_(1)` and `f_(2)` must be of opposite nature, `i.e.,` if one of the lenses is converging the other must be diverging. `(3)` If the achromatic combination is convergent, `f_(C)ltf_(D)` and as `(f_(C))/(f_(d))=(omega_(C))/(omega_(D)), omega_(C)ltomega_(d)` `i.e.,` in a convergent achromatic doublet, convex lens has lesses focal legth and dispersive power than the divergent one. Chromatic aberration of a lens can be corrected by :A. providing different suitable curvatures of its two surfaces.B. proper polishing of its two surfaces.C. suitably conbining it with another lens.D. reducing its aperture.