Video Transcript
A mirror rests on a flat
surface, seen from above. A light ray reflects from the
face of the mirror. A different incident ray is
then reflected from the same point on the mirror. Which color arrow correctly
shows the direction of the reflected ray for the new incident ray, which is
shown in red?
Okay, here we have a mirror
that’s represented by this solid line. This dashed line is
perpendicular to the mirror, and so this line is normal to the mirror. This is really important to
note because we use the normal line to define the angles that rays make when
reflecting. So we have an incident ray
represented by this black arrow. And the corresponding reflected
ray is shown by this black arrow here. But then, we also have a new
incident ray, which is shown by this red arrow. We need to think about the
direction that the corresponding new reflected ray would point and decide
whether that direction is shown by the blue or the purple arrow.
To figure this out, we just
need to remember the law of reflection, which states that any time light
reflects from a flat mirror, the angle of incidence is equal to the angle of
reflection. Let’s look again at the new
incident ray. We’ll mark out the angle that
it makes with the normal. And we can call this the new
angle of incidence. Let’s also mark out the angles
that the blue and purple arrows each make with the normal.
To answer this question then,
we just need to recognize which of these two angles is equal to the new angle of
incidence. If this isn’t clear by just
looking at the diagram, it’ll be helpful to notice that the new angle of
incidence is smaller than the angle of incidence made by this black arrow. So, because of the law of
reflection, we know that the new angle of reflection must be smaller than the
angle of reflection made by this black arrow.
Looking at the blue arrow, we
can see that it actually makes a larger angle. And therefore, the blue arrow
doesn’t follow the law of reflection. The purple arrow, however, does
follow the law of reflection. The purple arrow shows an angle
of reflection that is equal to the angle of incidence shown by the red
arrow. Therefore, we know that the
purple arrow correctly shows the direction of the reflected ray for the new
incident ray.
