Topic
23. Thin Lenses, part 2. Ray tracing rules.
The ray-tracing rules described in
this section can be used to find the position and size of an image given the
focal length of the lens and the position of the object. The rules depend on
the same approximations as for mirrors: the rules are valid only when the rays
strike the lens in the paraxial region (i.e., close to the central axis of
symmetry). In addition, the lens must be “thin,” which means that its thickness
must be small compared to its focal length. Many real-world lenses (such as
those in cameras) do not satisfy this condition exactly, but the general
principles of this section are still applicable.
Ray-tracing
rules for a converging (positive) lens:
1.
A ray that strikes the lens parallel to the axis is refracted through the lens
and passes through the focal point on the far side of the lens. (This is often
called the second focal point). See the top ray in the figure above.
2.
A ray that passes through the center of the lens emerges traveling in the same
direction with no change. See the middle ray in the figure above.
3.
A ray which passes through the first focal point (on the object side of the
lens) is refracted so that it emerges on the other side parallel to the axis of
the lens. See the bottom ray in the figure above.
Ray
tracing rules for a diverging (negative) lens:
1.
A ray that strikes the lens parallel to the axis is refracted through the lens
so that it appears to come from the focal point on the object side of the lens.
See the top ray in the figure above.
2.
A ray that strikes the lens heading for the focal point on the image side of
the lens is refracted through the lens so that it emerges parallel to the axis
on the other side. See the middle ray in the figure above.
3. A ray that strikes the lens in the center emerges traveling in the same direction on the image side. See the bottom ray in the figure above.
In
general, only two of the three rules are needed to locate the image, and the
most convenient pair of rules can be chosen in any situation.
The
fundamental assumption of these rules is that all of the rays from any
point on the object will reach the same point of the image: the rays that are
chosen are only examples that are easier to draw.