Chapter 45
Mirrors
Amirroris a reflective surface. By using curved mirrors, it is possible to form an opticalimageof a real
object. The simplest curved mirror is called aspherical mirror, so called because it can be thought of as
being a circle punched out of a hollow sphere that is silvered on one side. If we punch a circle out of a
hollow sphere that is silvered on theinside, we get aconcave mirror. If the sphere is instead silvered on the
outside, we get aconvex mirror. (Figs. 45.1 and 45.2.) The radius of the (imaginary) sphere that the mirror is
“punched out of” is called theradius of curvatureof the mirror. The point that would be at the center of this
sphere is called thecenter of curvatureof the mirror.
Ideally, to form a perfect image, the mirror should be in the shape of aparaboloid. However, spher-
ical mirrors are easier to manufacture, and can be almost as good, although the deviation from the ideal
paraboloidal shape does give rise to an optical defect called aspherical aberration, to be described later.
A concave mirror causes light to reflect in towards the axis of the mirror, and is called aconvergingmirror.
A convex mirror causes light to reflect away from the axis, and is called adivergingmirror.
Light coming from an object infinitely far away will come together at a single point in a concave (con-
verging) mirror; this point is called thefocusof the mirror, and the distance between the mirror and the focus
is called thefocal lengthof the mirror. It turns out that the focus is located half-way between the lens and the
center of curvature, so that we have
fDR
2
; (45.1)
wherefis the focal length andRis the radius of curvature.
The typical problem in mirror optics is this: we are typically given:
- The distance between the object and the mirror, called theobject distance,do.
- The “height” (size) of the object, called theobject height,ho.
- The focal length of the mirror,f. (Iffis not known, it can be determined from the radius of curvature
using Eq. (45.1).
We typically wish to find:
- The distance between the image and the mirror, called theimage distance,di
- The “height” (size) of the image, called theimage height,hi
- Themagnificationof the image,m. This is a dimensionless number that indicates how much bigger
the image is than the original object.