Defects in Lens

**Category : **JEE Main & Advanced

**(1) Chromatic aberration :** Image of a white object is coloured and blurred because \[\mu \] (hence f) of lens is different for different colours. This defect is called chromatic aberration.

\[{{\mu }_{V}}>{{\mu }_{R}}\] so \[{{f}_{R}}>{{f}_{V}}\]

Mathematically chromatic aberration =\[{{f}_{R}}-{{f}_{V}}=\omega {{f}_{y}}\]

\[\omega =\] Dispersive power of lens.

\[{{f}_{y}}=\] Focal length for mean colour \[=\sqrt{{{f}_{R}}{{f}_{V}}}\]

**Removal :** To remove this defect i.e. for Achromatism we use two or more lenses in contact in place of single lens.

Mathematically condition of Achromatism is : \[\frac{{{\omega }_{1}}}{{{f}_{1}}}+\frac{{{\omega }_{2}}}{{{f}_{2}}}=0\] or \[{{\omega }_{1}}{{f}_{2}}=-{{\omega }_{2}}{{f}_{1}}\]

**(2) Spherical aberration :** Inability of a lens to form the point image of a point object on the axis is called Spherical aberration.

In this defect all the rays passing through a lens are not focussed at a single point and the image of a point object on the axis is blurred.

** Removal :** A simple method to reduce spherical aberration is to use a stop before and infront of the lens. (but this method reduces the intensity of the image as most of the light is cut off). Also by using plano-convex lens, using two lenses separated by distance \[d=F-F'\], using crossed lens.

**(3) Coma :** When the point object is placed away from the principle axis and the image is received on a screen perpendicular to the axis, the shape of the image is like a comet. This defect is called Coma.

It refers to spreading of a point object in a plane \[\bot \] to principle axis.

**Removal :** It can be reduced by properly designing radii of curvature of the lens surfaces. It can also be reduced by appropriate stops placed at appropriate distances from the lens.

**(4) Curvature :** For a point object placed off the axis, the image is spread both along and perpendicular to the principal axis. The best image is, in general, obtained not on a plane but on a curved surface. This defect is known as Curvature.

** Removal :** Astigmatism or the curvature may be reduced by using proper stops placed at proper locations along the axis.

**(5) Distortion :** When extended objects are imaged, different portions of the object are in general at different distances from the axis. The magnification is not the same for all portions of the extended object. As a result a line object is not imaged into a line but into a curve.

** (6) Astigmatism :** The spreading of image (of a point object placed away from the principal axis) along the principal axis is called Astigmatism.

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