Question Video: Comparing Angles of Incidence to the Critical Angle | Nagwa Question Video: Comparing Angles of Incidence to the Critical Angle | Nagwa

Question Video: Comparing Angles of Incidence to the Critical Angle Physics • Second Year of Secondary School

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. [D] the blue angle and the green angle are both smaller than the critical angle.

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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 medium 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 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 blue ray shows how light is supposed to behave in a fiber optic cable, remaining inside the core as it propagates. Where the blue ray is incident on the cladding boundary, it experiences total internal reflection. But we can see that the green 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 grey 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 angle is greater than the critical angle and the green angle is smaller than the critical angle. This corresponds to answer option (A), which is our final answer. The blue angle is larger than the critical angle, but the green angle is smaller than the critical angle.

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