Video Transcript
The diagram shows light rays in
water being totally internally reflected at a boundary with air. The diagram also shows a light ray
in air incident on the same boundary and at the same angle of incidence. Which of the paths A, B, and C
would light incident on water from air follow?
The question asks us which of the
paths the light initially traveling in air would follow after being incident on the
boundary between air and water.
The diagram in the question shows
the direction of a light ray initially traveling in water before and after being
incident on the boundary between air and water. The direction of this ray after it
is incident on the boundary is the same direction as the direction shown by ray B on
the left half of the diagram. The question states that the light
ray initially traveling in air and the light ray initially traveling in water make
the same incident angle with the normal to the boundary between air and water.
Since the light ray initially
traveling in air and the light ray initially traveling in water are incident at the
same boundary at the same angle to the normal, then it might be guessed that after
being incident on the boundary the rays would travel in the same direction. This would mean that ray B would be
the path of the light ray initially traveling in air after it was incident on the
boundary between air and water. Let’s consider this
possibility.
In order for the correct answer to
be ray B, the light ray initially traveling in air would not change direction when
incident on the boundary between air and water. That is, the angle of incidence and
the angle of refraction would be equal. For a light ray not to change
direction at a boundary between two media, at least one of the following two things
must be true: the angle of incidence must be zero or the two media must have the
same refractive index. We can see that the angle of
incidence, 𝜃 sub i in the diagram, is not in fact zero. So, this first statement is not
true.
As for the second statement, we are
not given the refractive indices of air and water. Now, we might recall their
values. But even without this information,
we can deduce that the refractive index of water is greater than that of air. This can be worked out by observing
what happens to the light ray that is initially traveling in water before it is
incident on the boundary. The light ray that is initially
traveling in water does not pass into the air; instead, it is reflected back into
the water. This is called total internal
reflection.
Total internal reflection can occur
when a light ray is incident on a boundary between two media. In order for total internal
reflection to occur, the angle of incidence must be an angle greater than the
critical angle, 𝜃 sub c, for the boundary. This condition is necessary but not
sufficient. It must also be true that the
refractive index of the medium on the side of the boundary that the ray is initially
traveling in is greater than the index of the medium on the other side of the
boundary. That is, in this case, since the
light ray is initially in the water, then the refractive index of water must be
greater than the refractive index of air.
Let’s look again at the light ray
initially traveling in air. We have seen that it is not true
that the two media have the same refractive index. Since neither of these statements
are true, then it can’t be the case that the ray initially in air does not change
direction at the boundary. That means that ray B cannot be
correct. Having eliminated one possibility,
let’s clear some more space on screen.
Since the refractive index of water
is greater than the refractive index of air, then the angle of refraction must be
less than the angle of incidence. Looking at the path of ray A, we
can see that the angle of refraction is less than the angle of incidence. This tells us that the light ray
initially traveling in air could follow the path of ray A.
There is also the path of ray C to
consider. It is not always the case that a
light ray that is incident on a boundary between media only follows one path. It is possible for an incident ray
to produce two rays due to its interaction at the boundary. The ray that follows path C does
not enter the water. It reflects from the surface of the
water, just like the totally internally reflected ray that was initially in the
water. Looking at the totally internally
reflected ray, we can see that the angle this ray makes with the normal to the
boundary between air and water appears to be equal to the angle that the incident
ray makes with the normal. This is what must happen, according
to the law of reflection.
Now looking at the light ray
initially traveling in air along with ray C, we can see that both these rays also
appear to make equal angles with the normal to the boundary. We conclude then that ray C is the
ray that would be produced by the reflection of the light ray initially traveling in
air. Since we’ve already seen that ray A
would be produced by refraction of this incident ray, then we have found that both
ray A and ray C have directions that are possible for the light ray initially
traveling in air after it interacts with the boundary between air and water. Only ray B has a direction that is
not possible.
Our answer then is that ray A and
ray C show the paths that light incident on water from air would follow.
