## Spherical Aberrations:

The images formed by mirrors and lenses suffer from various defects because the theory of image formation is based on several approximations. For example, it is assumed that the aperture of the lens or mirror is small, and thus rays make small angles with the principal axis. As a result, theory gives a point image of a point object. However, in practice, it is not true. The rays incident on the lens surface at different distances from the principal Axis does not meet at the same point after refraction. Thus the image formed is blurred. Such a defect in an image is called spherical aberration. This defect is present even when monochromatic light is used.

Since the lens has a finite aperture, it produces a blurred disc-type image of a point object. The below figure shows the refraction of rays parallel to the principal axis from the convex and concave lens.

The rays close to the principal axis, called paraxial rays, are focused at the geometrical focus F of the length as given by the lens formula. The rays farther from the principal axis called marginal or peripheral rays are focused at a point F’ somewhat closer to the lens. The intermediate ryas focus on different points between F and F’. Thus, a three-dimensional blurred image is formed.

If a screen is placed perpendicular to the principal axis, the image obtained is not a point, but a disc. If the screen is moved parallel to itself, the disc has the least size at one position [shown as a dark line in figure (a)] The image form is best in this position. It has the least size and maximum intensity as compared to any other point. The periphery of the image in this position is called the circle of least confusion. Note that the size of images is large when the screen lies at F or F’. The distance FF’ is a measure of the magnitude of spherical aberration.

*The magnitude of spherical aberration for a lens depends on-*

- radii of curvature of the lens surface.
- distance of an object from the lens.

## Reducing the Spherical Aberration:

(1) For a given distance of an object from the lens, the spherical aberration can be reduced by properly choosing the radii of curvature [Aberration ∝ 1/f^{3}]. However, it cannot be reduced to zero.

(2) Another simple method is to use a stop (a circular opaque disc or annular disc) which blocks the rays either from the paraxial region (using a disc) or from the peripheral region (using an annular disc) as shown below. Since only a narrow pencil of rays passes through the lens, the aberration is reduced. A big disadvantage of this method is that the intensity of the image is substantially reduced.

(3) When using the plano-convex lens, the spherical aberration can be reduced if the total deviation suffered by rays is distributed over two surfaces instead of one. The below figure shows how the use of a plano-convex lens reduces the aberration. When light is incident on a curved surface, it suffers deviation on spherical as well as plane surface fig. (b) which is not the case when light is incident on plane surface fig. (a).

(4) Spherical aberration can also be reduced by using a combination of convex and concave lenses. Since aberration is the opposite for convex and concave lenses (F and F’ are reversed with respect to incident rays), a suitable combination can reduce the aberration to a small value. Higher theories of a combination of lenses prove that the spherical aberration can be greatly reduced if the distance between the two coaxial lenses is equal to the difference of their focal lengths.

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