Concave spherical mirror:
f = r/2
Convex spherical mirror:
f = ír/2
f = focal length
r = distance to center of curvature
What is the mirror’s focal
length?
f = ír/2
f = í (0.50 m)/2
f = í 0.25 m
31.10 - Parabolic mirrors
Parabolic mirrors provide a solution to the problem of
spherical aberration. Spherical aberration occurs
because some reflected rays do not pass precisely
through the focal point of a spherical reflector. The
farther the incident rays are from the mirror’s principal
axis, the more their reflected rays will miss the focal
point. The result is a blurry image.
Spherical aberration is a serious problem for
astronomers and others who need high quality
images. Astronomers use telescopes to create
images of distant objects. These telescopes often
include very large concave mirrors to collect as much
light as possible, allowing them to create images of
objects that are exceedingly dim. (And by “large” we
truly mean large: The diameter of a modern reflecting
research telescope is in the eight to ten meter range.)
If spherical mirrors were the basis of such telescopes,
the images they created would be blurry due to
spherical aberration.
To produce a sharp image, some telescopes instead use a mirror that has a cross section in the shape of a parabola rather than a section of a
circle. Why? Reflected rays from distant objects converge to form a sharp image, no matter how far the incident ray is from the principal axis.
This telescope mirror is a hexagonal mosaic of smaller spherical
mirror segments. Note the workman sitting at the focal point.