Rays close to the axis of the mirror are brought to
a focus at one point but those far from the axis meet at a range of different points. The effective
focal length varies for rays at different distances from the axis (See Figure 1).
This is
called Spherical Aberration and the locus of the focal points
is known as a caustic curve. You can see this on the surface of tea or coffee in a mug. (Figure
2). This defect means that large spherical mirrors are not good for giving a focused image over
a wide field of view.
For all spherical
mirrors the mirror formulae only work and there is therefore only ever a perfectly sharp image
when all the rays are parallel to the axis and close to it - in fact along the axis.
The
image actually gets more and more fuzzy the further from the axis we go. This limits the field of
view and is a serious problem for astronomical telescopes where the large aperture is essential
for maximum light gathering power.
With a spherical mirror and with a wide incident
beam, the light is not focused to one point but forms a pattern, the envelope of which is called a
caustic curve (see earlier).
There are three solutions:-
(a) use a parabolic mirror
(See: Parabolic mirrors)
(b) use a spherical mirror
but with a specially shaped glass correcting plate in the path of the incident beam
(See: Schmidt telescopes)
(c) reduce the aperture of the
mirror by using a stop (e.g a piece of card with a hole in it)