Video Transcript
In this video, we’ll be talking
about how to explain the directions of light rays reflected from flat mirrors. We’ll soon learn about the very
simple, yet very important, rule that determines just how light gets reflected from
a mirror like this. But first, let’s get started by
reviewing some basic information about light and how it travels.
Recall that in order to see an
object, light must somehow travel directly from that object into our eye. For an object that emits light,
such as a phone screen, we can simply see the light that is produced by the
object. But for an object that doesn’t
produce light, like a book, we can only see the object if light from some light
source, such as the Sun or a light bulb, reflects off of that object and into our
eyes. To learn about the reflection of
light, we’ll need a simple way to represent light and how it travels, so it’ll be
helpful to be able to single out one ray of light at a time.
So, what exactly is a light
ray? To answer this, let’s first recall
that light is an electromagnetic wave. So, imagine we’re looking at the
top of a light bulb. Light waves travel away from the
bulb in all directions. And we’ve used arrows to represent
some of these directions. Each of these arrows is a ray. A light ray is an arrow that we use
in diagrams to show the direction in which light waves travel. It’s important to understand that a
light ray is not something that can actually be seen in real life.
Rays only exist in diagrams, but
still they’re incredibly useful for learning about the reflection of light. One way that they’re useful is that
they show the fact that light travels in straight lines. So we’ll never see a light ray that
looks like this or this. Light rays only point in straight
lines, as light only travels in straight lines. Rays are also really useful to us
because we can see them from the side. In real life, we can only see light
that travels directly into the eye. So, say this eye represents our
perspective. We would see the light that is
represented by this ray, which points into the eye. But we would not see the light that
is represented by any of these other rays, since those do not point into the
eye. In a diagram, however, rays allow
us to clearly see where light is traveling, no matter the direction.
Now, let’s think about a diagram
that shows one single light ray. The ray points in a straight line
since light only travels in straight lines. But that doesn’t mean that this ray
will go on forever in this direction. For instance, the light represented
by the ray could get reflected from a surface, such as a mirror. Now, when we use a mirror in
everyday life, we usually hold the mirror so that we’re looking at it face-on, as if
we could see our own reflection in it. But in the diagrams we’ll be using
for this lesson, we often imagine the mirror like it’s been turned sideways, so that
we’re looking at its edge, rather than its surface.
So in the diagram, the mirror is
represented by just a solid line. Keeping this in mind, let’s erase
the hand to make this diagram as clear and simple as possible. So now we just have a mirror and
this one light ray. If we extend the path of the ray,
we see that the light will eventually reach the face of this mirror and reflect. When light reflects, the path of
the light changes, but the path itself is still made up of straight lines. We’ll consider the light before and
after it’s been reflected separately. So, we say that this is a ray and
that this is a ray. The ray that points toward the
mirror, shown here, is known as the incident ray, where incident is just another way
to say that something hits a surface. This other ray is known as the
reflected ray, since it’s been reflected and points away from the mirror.
Now, we might notice that the
mirror and rays in this example diagram have some symmetry to them. And indeed, we can draw in a dashed
line to help show this symmetry. It turns out that a line like the
one we’ve drawn here is key to our understanding of how light reflects from a
mirror. We say that this line is normal to
the face of the mirror, where normal just means perpendicular, or at a 90-degree
angle, to. So for instance, say we have a
mirror that looks like this. A line normal to the mirror would
look like this, since a normal line is simply perpendicular, or normal, to the
mirror. Now, the normal line is very
important because we use it to measure the angles that rays make when reflecting
from mirrors. In fact, all angles that we measure
should be measured with respect to a normal line.
To see what we mean by this,
suppose that light is incident on the mirror like shown here. This is the incident ray. The angle between the incident ray
and the normal line is called the angle of incidence. We know that there must also be a
reflected ray, which looks like this. The angle between the reflected ray
and the normal is called the angle of reflection. Let’s use a protractor to measure
both angles. First off, we need to line up the
protractor correctly. And there are different ways we
could do this, so long as we’re careful. Here, we’ve placed the protractor
so that this line on the bottom edge of the protractor lies horizontally, along the
edge of the mirror. The line perpendicular to this is
vertical then and aligned with the mirror’s normal. Where these lines meet on the
protractor is the center point of the protractor.
Notice that this protractor is a
semicircle. If it was a complete circle, its
center would be here. When placing the protractor, this
point is most important: the center point needs to be lined up with the point on the
mirror where the light rays touch the mirror.
Now that we’ve done this, it’s just
a matter of reading the protractor scale correctly. Let’s try it. We’ll measure the angle of
incidence first. So here is the incident ray. Looking closer at the ray, it
appears to be exactly aligned with the 50-degree mark on the outermost scale of the
protractor. But this doesn’t mean that the
angle of incidence equals 50 degrees. That’s because the zero mark of the
scale is down here, aligned with the edge of the mirror. So the angle of 50 degrees is
really measured between the incident ray and the mirror. But we know that the angle of
incidence must be between the incident ray and the normal. And the normal is aligned with the
90-degree mark. Therefore, we need to subtract 50
degrees from 90 degrees. So the angle of incidence is equal
to 40 degrees.
Next, let’s measure the angle of
reflection. The reflected ray appears to be
exactly lined up with the 130-degree mark on the outer scale. So, to measure the angle between
the ray and the normal, we subtract 90 degrees from 130 degrees, which equals 40
degrees. So we’ve found that the angle of
incidence is equal to the angle of reflection. This is no coincidence. In fact, this relationship is known
as the law of reflection. And it holds true any time light
reflects from a flat mirror.
The law of reflection states that
the angle between the incident ray and the line normal to the mirror is equal to the
angle between the reflected ray and the line normal to the mirror or, in more simple
terms, that the angle of incidence equals the angle of reflection. Further, it’s important to note
that the incident ray, the reflected ray, and the normal all lie in the same
plane.
Now, the law of reflection is the
key factor in determining the directions in which light rays reflect. And thankfully for us, it’s very
simple. If, for instance, we see an
incident ray that makes an angle of 20 degrees with the normal, then we know that
the corresponding reflected ray must also make an angle of 20 degrees with the
normal. And if the light source happened to
move so that the angle of incidence increased to, say, 60 degrees, then the
reflected ray would adjust too, so that the angle of reflection is then 60
degrees. It’s that simple. To get some more practice with
these new concepts, let’s work through a few example questions.
The diagram shows how a
protractor is used to measure the angles of incidence of two rays. Which color arrow shows the ray
with the greater angle of incidence?
Alright, so we have two
different rays incident on a flat mirror. The mirror is represented by
this solid vertical line. This question is asking about
angles of incidence. So let’s recall that the angle
of incidence is the angle between an incident ray and the line normal to the
face of the mirror, where normal just means perpendicular. This horizontal dashed line
then is normal to the mirror. So the angles of incidence are
the angles that the arrows make with this line. We can use the protractor to
measure these angles. And first thing, we should
notice that the normal line is at the zero-degree mark on the outer scale of the
protractor. This means that any angle we
measure with respect to this zero mark will be measured with respect to the
normal line, which makes our job fairly easy.
Let’s take a closer look at
where the arrows meet this scale on the protractor. We’ll start with the red
arrow. The red arrow is just slightly
beyond this medium-sized line that’s directly between the marks of 30 degrees
and 40 degrees. This medium-sized line then
marks 35 degrees. Looking a little closer at the
red arrow, we can see that it’s aligned with the first small line past the
35-degree mark. Each one of these small lines
corresponds to one degree. And therefore, we know that the
angle of incidence shown by the red arrow is 35 degrees plus one degree or 36
degrees.
Next, let’s look at the purple
arrow. This arrow is just a little bit
before this middle-sized line between the marks of 50 and 60 degrees. So it’s just before the
55-degree mark. More specifically, the purple
arrow is one small line before the 55-degree mark. So we know that it shows an
angle of incidence of 54 degrees. 54 degrees is greater than 36
degrees, so we’ve found that the purple arrow shows the ray with the greater
angle of incidence.
Let’s look at another example
involving angles.
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.
Next, we’ll do one more question
involving the reflection of light.
A vertical mirror rests on a
flat horizontal surface. The orange arrow shows the
incident light ray on the mirror. Which of the following is
true? (A) The direction of the
reflected ray must be as shown by the red arrow. Or (B) the direction of the
reflected ray could be as shown by either the red arrow or the blue arrow.
To answer this question, we’ll
need to understand what the difference is between the red arrow and the blue
arrow. So let’s go over exactly what’s
being shown in the diagram. We know that this mirror stands
vertically and that this flat surface is horizontal. Notice this dashed line that’s
perpendicular to the face of the mirror. This line represents the normal
to the mirror, and it lies in the same horizontal plane as the flat surface. The orange arrow, which
represents the incident ray, and the red arrow also lie in the horizontal
plane. The blue arrow, however, looks
a little different. The blue arrow starts here at
the same point on the mirror as the red arrow, but it appears to rise up out of
the horizontal plane. That’s why we see this dotted
line. It’s there to show us that the
blue arrow rises up above the red arrow.
To see this better, we can draw
a side view of the diagram. This green line represents the
horizontal surface or the plane where the incident ray and the normal line
lie. This line represents the
mirror, which stands vertically. We can see that the blue arrow
starts here at the bottom of the mirror and points upwards by some amount. Therefore, the blue arrow does
not lie in the horizontal plane.
Now, the key to answering this
question is to simply recall that for light reflecting off a flat surface, the
incident ray, the normal to the surface, and the reflected ray must all lie in
the same plane. We know that the incident ray
and the line normal to the mirror lie in the horizontal plane. So the reflected ray also has
to lie in this plane. The red arrow lies in this
plane, but the blue arrow does not. Therefore, we know that the
blue arrow could not show the direction of the reflected ray. So answer option (A) is
correct. The direction of the reflected
ray must be as shown by the red arrow.
Now that we’ve had some practice,
let’s take a moment to reflect on what we’ve learned.
In this lesson, we saw how light
can be represented by rays, which are arrows in diagrams that show the direction in
which light waves travel. But we need to remember that a
light ray isn’t something that can actually be seen in real life. We also learned that light always
travels in straight lines. Light, of course, can be redirected
if it gets reflected from a surface. And in that case, the incident and
reflected rays both still point in straight lines.
We saw how to measure the angles
that these rays make and how all angles should be measured with respect to a line
normal, or perpendicular, to the surface. The angle between the incident ray
and the normal is known as the angle of incidence. The angle between the reflected ray
and the normal is known as the angle of reflection. The law of reflection states that
the angle of incidence must be equal to the angle of reflection and that the
incident ray, reflected ray, and the normal all lie in the same plane.
