Unformatted text preview: • A ray that reﬂects from the mirror after passing through the center of curvature C returns
along itself (ray 3 in ﬁgure 44).
• A ray that reﬂects from teh mirror at point c is reﬂected symmetrically about that axis (ray
4 in ﬁgure 44). Figure 44: Tracing Rays for Spherical Mirrors 15.3 Thin Lenses In many ways thin lenses are just like mirrors. They have the same relationship between their
object and image distances
and most of the ray tracing procedures are exactly parallel to the spherical mirror ray tracing rules.
The focal length of a lens is somewhat more complicated
= (n − 1)
r2 r2 where r1 is the radius to the side of the lens closest to the object and r2 is the radius of curvature
further from the object. Note that the we must be careful to use the proper sign with the radii of
curvature. As has been the trend with signs in the rest of this chapter, if the center of the radius
is on the opposite side of the lens than the object then it is negative and vice versa if it is on the
same side. Also note that a thin lens has two focal points, one on each side of the lens but both
the same distance away.
Similar to the convex and concave mirrors of the last section, we will see that lenses come in
a converging and a diverging variety. In ﬁgure 45 we can see why the two types of lenses act
The ray tracing procedures for lenses are very similar to those for spherical mirrors and the ray
tracing technique can be employed with the same utility.
• A ray that is initially parallel to the central axis of the lens will pass through (or look as if it
passed through) the focal point on the far (near) side of the lens for a converging (diverging)
• A ray that initially pass through (or is heading towards) the focal point on the near (far)
side of the lens will emerge parallel to the central axis for a converging (diverging) lens.
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- Spring '08
- Physics, ray tracing, Curved mirror