Which of the mirrors below is a
spherical concave mirror? Incident light is shown by the
orange lines. Is it (A), (B), (C), or (D)?
To start, we should remember that
for a concave mirror, the focal point is on the same side of the mirror as the
center of curvature. That is, the reflective surface is
on the inside curve of the mirror. Just knowing this, we can eliminate
answer options (A) and (B), since these seem to reflect light from the surface on
the outside of the mirror’s curvature, making them convex rather than concave.
We should also keep in mind that
the mirror should have spherical curvature. Recall that if we cut away a
portion of a sphere, we should see a line that bends with constant curvature. So we know that every point on a
spherical mirror’s surface is equidistant to the mirror’s center of curvature. This description fits the mirror
shown in option (C).
We can infer that the mirror’s
center of curvature is here. And notice that any lines we draw
between the center of curvature and the surface are the same length. We cannot say the same for option
(D), though. This surface seems to follow a more
elliptical shape. And therefore we can’t even define
a center of curvature that’s of equal distance from all points on the surface. Let’s eliminate this option.
Thus, we know that the correct
answer is (C), as it’s the only option that shows a spherical concave mirror.