Video Transcript
The following figure shows two
light rays from the same point on an object that are incident on a concave
mirror. The distance that the rays travel
from the point to the surface of the mirror is greater than the distance from the
center of curvature of the mirror to its surface. A real image is produced. What is the location of the
image? (A) At the surface of the
mirror. (B) At the focal point of the
mirror. (C) At the center of curvature of
the mirror. Or (D) between the focal point and
the center of curvature of the mirror.
Before we begin, let’s take a
closer look at the diagram. Here is the concave mirror, and we
can see that its focal point and center of curvature have been marked. We also have two light rays shown
in red and blue. Notice that they both originate
from the same point on the object here but that they travel in different
directions. The ray shown in red travels
horizontally at first and is then reflected off the surface of the mirror at an
angle. Notice that the reflected red ray
travels directly through the mirror’s focal point. The ray shown in blue travels
diagonally and is incident on the mirror such that the reflected ray travels back
along the same path as the original incident ray. Note that the blue ray passes
directly through the center of curvature of the mirror.
In this question, we’ve been asked
to figure out where the image is produced by these two rays. To do this, let’s clear some room
on screen and remember some information about light rays and concave mirrors. First, recall that concave mirrors
can produce both real and virtual images. But here, we were told that a real
image is produced. Recall that a real image is formed
where light rays intersect or cross paths and that real images formed by a concave
mirror are inverted, meaning they are appear upside down. Knowing this, in order to determine
where this image is formed, we simply have to determine where the rays cross
paths.
Now, don’t be fooled by answer
option (A). While it is true that both rays do
reflect off of the surface of the mirror, they reflect at different points that are
quite far away from each other. So they don’t intersect there. So this isn’t where the image is
formed. We should eliminate answer choice
(A). Next, (B) says that the focal
point, and the red ray does pass through the focal point. But the rays don’t intersect here,
so we can eliminate this answer choice.
Similarly, for option (C), the blue
ray does pass through the mirror’s center of curvature, but the red ray doesn’t, so
they don’t cross paths here. And thus, we should eliminate this
option as well. Instead, we can see that the rays
cross paths here, in between the center of curvature and the focal point. So we know that option (D) is
correct. The image is produced between the
focal point and the center of curvature of the mirror.
Remember too that because this is a
real image formed by a concave mirror, the image is inverted. That’s why these rays, which
originate up here at the top of the object, intersect all the way down here, closer
to the bottom of the object, as the image appears upside down.
