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 in a medium with a higher
refractive index and is incident on 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. 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. So in the diagram we’ve been given, the blue and green rays each show how a light ray
is supposed to behave in a fiber optic cable, remaining inside the core as it
propagates. Each time either ray is incident on the cladding boundary, it experiences total
internal reflection.
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 blue and green angles are larger than the critical angle. This corresponds to answer option (C), which is our final answer. The blue angle and the green angle are both larger than the critical angle.
