To locate the image, we start with three rays emanating from the top of the object: in this case, the top of the penguin’s head. The rays reach
the mirror at three different points. They then reflect and converge. The point at which they converge is the location of the top of the image
penguin’s head.
With hand-drawn ray-tracing diagrams, we use the working approximation that the incident rays are paraxial, so that they converge at one
point. In the simulations in this chapter, you can observe accurate ray-tracing diagrams that display the effects of spherical aberration.
Below, we show each ray separately; all three rays and the image are shown in Concept 5.
Ray 1 starts as an incident ray that is parallel to the principal axis. It reflects off the mirror and passes through the focal point after it reflects.
Ray 2 starts as an incident ray that passes through the focal point and then reflects parallel to the principal axis.
Ray 3 begins as an incident ray that passes through the center of curvature, strikes the mirror perpendicularly, and reflects back, moving along
the same line as the incident ray.
Why do these rays reflect in the way they do? The first incident ray is parallel to the principal axis. By definition, the reflection of this ray passes
through the focal point.
The second ray is parallel to the principal axis after it reflects. The definition of focal point applied “in reverse” explains why this should be so:
Since the ray passes through the focal point before it reflects, it is parallel to the axis after it reflects.
The final ray reflects straight back because, like a radius of the sphere, it meets the spherical surface perpendicularly. Its angle of incidence is
zero degrees, so its angle of reflection will be the same.
Ray 1
Incident parallel to axis, reflects through
focal pointRay 2
Incident through focal point, reflects
parallel to axisRay 3
Incident through center of curvature,
reflects straight back