Video Transcript
The following figure shows two
light rays from the same point on an object that are incident on a concave
mirror. The object is between the center of
curvature of the mirror and the focal point of the mirror. A real image is produced. Which of the following is the
location of the image? (A) Between the focal point and the
center of curvature of the mirror. (B) At the center of curvature of
the mirror. (C) At the focal point of the
mirror. (D) At the surface of the
mirror. Or (E) at a distance from the
surface of the mirror greater than the distance to the center of curvature of the
mirror as measured parallel to its optical axis.
An image is the point where
reflected rays with the same origin intersect. Here, we have two reflected rays,
which have the same origin. So, we must look at the reflected
rays and see where they intersect. None of the reflected rays
intersect in the region between the center of curvature and the focal point. So, option (A) can be
eliminated.
The center of curvature contains no
rays passing through it, neither incident nor reflected. So, option (B) can be eliminated as
well.
We see that only one reflected ray,
the red one, passes through the focal point. The blue incident ray passes
through it. However, its reflected ray is what
helps makes up the image, but this does not pass through the focal point. Therefore, option (C) can be
eliminated.
It is true that there are rays at
the surface of the mirror. However, the reflected rays do not
intersect at the surface of the mirror. So, option (D) can be ruled
out.
All light rays from the origin that
are reflected by the mirror will meet at the point where the real image is
produced. We can see that the two reflected
rays meet at this point that we will call point 𝑃, and this is where the image is
produced. If we look at the distance between
the surface of the mirror and its center of curvature along the optical axis of the
mirror and compare it to the distance from the surface of the mirror to point 𝑃
along the optical axis of the mirror, we can see that point 𝑃 is further from the
surface of the mirror than the distance from the surface of the mirror to its center
of curvature.
Therefore, the correct answer is
option (E). The location of the image is at a
distance from the surface of the mirror greater than the distance to the center of
curvature of the mirror as measured parallel to its optical axis.
