Video Transcript
A light ray travels along an optical fiber by total internal reflection, as shown in
the diagram. The light reflects from the internal surface of the fiber at an angle very slightly
greater than the critical angle. What is the most correct description for what happens at point P if light is sent
into the fiber when the fiber is bent? (A) The light totally internally reflects at P because the angle of incidence there
is greater than the critical angle. (B) The light totally internally reflects at P because the angle of incidence there
is less than the critical angle. (C) Some of the light is transmitted out of the fiber at P because the angle of
incidence there is greater than the critical angle. (D) Some of the light is transmitted out of the fiber at P because the angle of
incidence there is less than the critical angle. (E) Some of the light is refracted along the fiber surface at P because the angle of
incidence there is equal to the critical angle.
Let’s begin by clearing some room on screen and refreshing our memories about the
critical angle, total internal reflection, and how light travels along an optical
fiber.
Typically, when light is incident upon a medium boundary — that is, the surface
separating two media of different optical densities — some of the light reflects at
the boundary and some of the light transmits, or passes through, and refracts. To help visualize this, think about walking down the street and passing by a window
that we can both see through into the building and that we can also see our own
reflection in. But in the case of a light ray that’s traveling through a higher-density material and
reaches the surface of a less dense material, the light ray will be entirely
reflected if its angle of incidence is greater than the critical angle. This is total internal reflection.
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. Thus, in the diagram we’ve been given, this part up here shows how light is supposed
to behave in a fiber optic cable, remaining inside the core as it propagates.
Each time the ray is incident on the cladding boundary, it experiences total internal
reflection. But we want to know what happens down here at point P, where the cable is bent. This dashed line represents the normal, or perpendicular, line to the surface at the
point where the light is incident. Let’s draw a close-up view to see this better. Remember that a light ray’s angle of incidence is always measured with respect to the
surface normal. So, looking at the angle this light ray makes with the normal, we can see it’s very
small — much smaller than the angles we see up here where the light is totally
internally reflected.
Since this angle here is said to be just barely greater than the critical angle, we
know that this little angle at point P is definitely less than the critical
angle. Thus, we can eliminate answer options (A) and (C) because they suggest that it’s
greater than the critical angle. And we can also eliminate (E) since it suggests that the angles are equal. We can also tell that option (B) is incorrect because total internal reflection only
occurs when the angle of incidence is greater than the critical angle, not less than
the critical angle.
This leaves us with option (D), which is the correct answer. Some of the light is transmitted out of the fiber at P because the angle of incidence
there is less than the critical angle.
