Week 12: Lenses and Mirrors 397
to an apparent point of divergence in space from the image, we can see the imageexactly
as ifwe were looking at an object.
In the case of a plane mirror (above) the image is alwaysbehindthe mirror. The light
rays you see do not actually pass through the image, they simply appear to diverge from
it. We call such an image avirtualimage.
We need to define several quantities that will be essential in our analysis of how lenses
and mirrors work. The distance from a mirror (or lens) to an objectone is viewing in
(or through) it iss, theobject distance. Object distances arepositiveif the object is
on the side of the mirror (or lens) that the light is comingfrom. Object distances are
obviously ‘always’ positive, unless the object is avirtual objectformed out of the image
of a previous mirror or lens, which can be either positive or negative.
The distance from a lens or mirror to the image one is viewing iss′, theimage distance.
Image distances arepositiveif the image is on the side of the mirror (or lens) that the
light is goingto.
Multiple mirrors can be used to create images of images, or images of images of images
(used as “virtual objects” for the second mirror). Most of us have experienced the
“infinite tunnel” of images that results from standing directly in between two plane
mirrors.image P’image P’object Pimage P" of image P’Figure 157: Two mirrors create an image of an image. Only a few of themany rays are drawn –
copy the picture and fill in more yourself.
12.2: Curved Mirrors
Plane mirrors simply create a perfect image of everything that is in the real space reflected
in the mirror. Things get more interesting if the mirrors arecurved. Curved mirrors can
create images that are systematically larger or smaller than the object, and can create a
new kind of image from the one seen in figure (156).
In figure (158) we see aconcave spherical mirror, which we will also call aconverging
mirror or apositivemirror^108. The horizontal line running through the center of the mir-
ror is very important and is called theaxisof the mirror, which is rotationally symmetric
about this axis. Even imaging an arrow is too complicated for our purpose (which is to
figure out how spherical mirrors can make images at all) so we look forthe image of a
single pointP, which we locate for convenience on the axis of the mirror.
The image P’ occurs where two reflected rayscross. The two rays in question are the
one that strikes a distancelup the mirror (with angle of incidence equal to the angle of(^108) For those who have concave/convex dyslexia, remember that concaveis like a cave, and curves inward, while
convexis nothing at all like a vex. What is a vex, anyway?