Video Transcript
The diagram shows two different
light rays propagating through an optical fiber cable. Two angles are shown, one in green
and one in blue. Which of the following statements
about these angles is correct? (A) The blue angle is larger than
the critical angle, but the green angle is smaller than the critical angle. (B) The blue angle is smaller than
the critical angle, but the green angle is larger than the critical angle. (C) The blue angle and the green
angle are both larger than the critical angle. Or (D) the blue angle and the green
angle are both smaller than the critical angle.
Let’s begin by clearing some room
on screen and reminding ourselves about the critical angle and how light rays travel
through an optical fiber cable like the one shown here. Note that both of these topics
consider light that travels from a medium with higher refractive index to a boundary
with a material of lower refractive index.
First, let’s recall that when a ray
of light is incident on a medium boundary at an angle greater than the critical
angle, it will undergo total internal reflection. In this case, none of the light
transmits or passes through the boundary, since it’s entirely reflected. So, if a ray’s angle of incidence
is greater than the critical angle, it will experience total internal
reflection. But if light is incident at an
angle less than the critical angle, it will transmit and refract as usual.
Fiber optic cables are a very
useful application of total internal reflection. In such a cable, light travels
through a central fiber core surrounded by a cladding that’s made of a material with
a lower index of refraction than the core. Then, as the light travels down the
fiber, it repeatedly reflects off the cladding boundary to stay within the core. Then, eventually, the light emerges
from the other end of the cable.
Thus, in this diagram we’ve been
given, the green ray shows how light is supposed to behave in a fiber optic cable,
remaining inside the core as it propagates. Each time the green ray is incident
on the cladding boundary, it experiences total internal reflection. But we can see that the blue ray
escapes the core at this point here. It transmits and refracts at the
cladding boundary. So we know it does not experience
total internal reflection here.
Now, let’s look at the two angles
we’re considering in this question. We can see that they’re each
measured with respect to a gray dashed line. That line represents the normal to
the medium boundary at the point where the ray is incident. So the two angles are angles of
incidence.
We’ve already established that if
the angle of incidence is greater than the critical angle, we will see total
internal reflection. And if the angle of incidence is
less than the critical angle, we will see the ray transmit and refract.
Thus, we know that the green angle
is greater than the critical angle and the blue angle is smaller than the critical
angle. This corresponds to answer option
(B), which is our final answer. The blue angle is smaller than the
critical angle, but the green angle is larger than the critical angle.
