Question

Answer the following question.

Explain spherical aberration for spherical mirrors. How can it be minimized? Can it be eliminated by some curved mirrors?

Answer 1

1. In the case of spherical mirrors (excluding small aperture spherical mirror), The rays coming from a distant object farther from the principal axis do not remain parallel to the axis. Thus, the focus gradually shifts towards the pole.
2. The assumption for clear image formation namely, ‘If there is a parallel beam of rays, it is paraxial, i.e., parallel and close to the principal axis’, is not followed in this case.
3. The relation `("f" = "R"/2)` giving a single point focus is not followed and the image does not get converged at a single point resulting in a distorted or defective image.
4. This phenomenon is known as spherical aberration.
5. It occurs due to the spherical shape of the reflecting surface, hence known as spherical aberration.
6. The rays near the edge of the mirror converge at focal point F_M. Whereas, the rays near the principal axis converge at point F_P. The distance between F_M and F_P is measured as the longitudinal spherical aberration.
7. In spherical aberration, a single-point image is not possible at any point on the screen and the image formed is always a circle.
8. At a particular location of the screen (across AB in the figure), the diameter of this circle is minimum. This is called the circle of least confusion. The radius of this circle is transverse spherical aberration

Remedies for Spherical Aberration:

1. Spherical aberration can be minimized by reducing the aperture of the mirror.
2. Spherical aberration in curved mirrors can be completely eliminated by using a parabolic mirror.