Video Transcript
Does the following figure correctly
show the reflection of light rays from a plane mirror producing an image of the
object in front of the mirror?
This question has a figure, or
diagram, depicting an object in front of a plane mirror. Two parallel light rays from two
different points on the object are incident on and then reflected from the
mirror. The figure also shows an image of
the object. Now the question asks us whether
the figure correctly shows the reflection of light rays and the production of an
image by a plane mirror.
To answer the question, we need to
check two things: whether the light rays are correctly shown and whether the image
is correctly shown. So let’s first consider the light
rays. When a light ray — let’s take this
one, for example — reflects from a plane mirror, then the angle of incidence —
that’s the angle between the incident ray and the normal line to the mirror, which
is shown here in yellow — will be equal to the angle of reflection, which is the
angle between the reflected ray and the normal line to the mirror.
Now, in this case, the mirror is
vertically oriented. So any normal line to the surface
of the mirror will always be horizontal. Drawing the angles of incidence in
pink and the angles of reflection in blue for both our light rays, we can see that
for both of them, the pink angle of incidence is equal to the blue angle of
reflection. This is all we need in order to say
that the paths of the incident and reflected rays are drawn correctly.
So now that we’re happy with how
the light rays are drawn, let’s think about whether this image of the object is
drawn correctly. One way to check this is to recall
that the distance between a point on the object and the mirror is equal to the
distance between the corresponding point on the image and the mirror. So, if we pick a point on the
object — let’s say here, for example — we can see that the distance between this
point and the mirror is the same as the distance between the mirror and the
corresponding point on the image of the object. We can also see that the same is
true for any other point on the object.
Another way we can check that the
image is drawn correctly is to recall that light rays always appear to travel in
straight lines. This means that when these light
rays enter an observer’s eyes, the observer will see an image consistent with the
light rays having apparently traveled in straight lines. These straight-line paths are shown
by the dotted lines on the diagram. This means that to an observer,
light from this point on the object will appear to have originated from here. Similarly, light from this point on
the object will appear to have originated from here.
Using these methods of checking, we
can see that the figure shows the image with the correct size, shape, and position
that we’d expect. We can conclude then that the
correct answer to the question is yes. The figure correctly shows the
reflection of light rays from a plane mirror producing an image of the object in
front of the mirror.
