Video Transcript
Four identical light rays travel
through water and then pass through objects made of different materials. The materials of the objects all
have different densities and light travels at different speeds in them. In which of the following objects
does light travel at the greatest speed?
This is a question about light
entering and then leaving a substance that has a different density to the medium it
was originally traveling through. The question tells us that all the
gray blocks have different densities to each other. To answer this question, we need to
use the different paths taken by the incident light rays through the blocks to
identify which ray has the greatest speed. Importantly, each of the four light
rays enter the new medium at the same angle and location. This means we know that any
difference in their path through the new medium will be because of their difference
in speed caused by the different densities of the new media.
Let’s remember that refraction is
the change in direction of light that we’re seeing here. Refraction occurs as light passes
from one medium to another. This is because light travels at
different speeds in different media. When light travels from a medium of
lower density to a medium of higher density, the ray bends towards the normal as the
light slows down. The greater the change in
densities, the greater the speed and direction change. When light travels from a more
dense medium to a less dense medium, the ray bends away from the normal as the light
speeds up. Again, the greater the change in
density, the greater the speed and direction change, this time away from the normal
rather than towards it.
In all four diagrams, the light is
refracted twice. This is because the light enters a
different medium two times. The first refraction occurs when it
enters the gray block. The second time the light is
refracted occurs when it leaves the gray block. We’re looking for the object in
which the light travels at the greatest speed. So, looking at the first direction
change, when the light enters the object, we need to identify the object in which
the ray experiences the greatest direction change away from the normal.
In diagram (A), we see that the ray
is bent towards the normal rather than away from it. That is, the angle 𝜃 r between the
refracted ray and the normal is smaller than the angle 𝜃 i between the incident ray
and the normal. The same is true in diagrams (B)
and (D), although we can note that the direction change is barely noticeable in
diagram (B). That indicates that the medium here
is close in density to the surrounding medium, and so the change in speed is
small. In diagrams (A), (B), and (D) then,
the speed of the light decreases in the object.
Diagram (C) is the only diagram
that shows the light bending away from the normal as it enters the object. That is, diagram (C) is the only
one in which the angle of refraction 𝜃 r is greater than the angle of incidence 𝜃
i. Since the light bends away from the
normal as it enters the object, then this means that the speed of light increases in
the object in diagram (C). Since diagram (C) is the only case
in which the speed of light increases in the object as compared to its speed in the
surrounding water, then this must be the object in which the light travels at the
greatest speed.
Therefore, our answer to this
question is diagram (C).
