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Chapter 9: Problem 31

What is total internal reflection, and how is it related to the critical angle?

Short Answer

Expert verified
Answer: The relationship between total internal reflection and the critical angle is that total internal reflection occurs when the angle of incidence is greater than the critical angle. In this situation, the light wave does not transmit or refract into the second medium and is instead entirely reflected back into the first medium due to the refractive indexes of the two media and the angles of incidence involved.

Step by step solution

01

Definition of Total Internal Reflection

Total internal reflection (TIR) is a phenomenon that occurs when a light wave traveling from a medium with a higher refractive index to a medium with a lower refractive index reaches the interface at an angle greater than the critical angle. At this angle, instead of being partially refracted and transmitted into the second medium, the light is entirely reflected back into the first medium.
02

Critical Angle

The critical angle is the angle of incidence (measured from the normal to the interface between the two media) at which the refracted light, or the transmitted ray, exits parallel to the interface. Any angle of incidence greater than the critical angle will lead to total internal reflection.
03

Calculating the Critical Angle

To calculate the critical angle, we can use Snell's Law (\sin{i} = n_2/n_1 * \sin{r}). In the case of the critical angle, the angle of refraction (r) will be 90 degrees (the transmitted ray is parallel to the interface). Plugging this into Snell's Law, we get: \sin{i_c} = n_2/n_1 * \sin{90} Where i_c is the critical angle, n_1 is the refractive index of the first medium (higher), and n_2 is the refractive index of the second medium (lower).
04

Relationship between Total Internal Reflection and Critical Angle

The relationship between total internal reflection and the critical angle is that TIR occurs when the angle of incidence is greater than the critical angle. When this condition is met, the light wave cannot be transmitted or refracted into the second medium; instead, it is entirely reflected back into the first medium. This is due to the refractive indexes of the two media and the angles of incidence involved. The light is unable to "escape" the higher refractive index medium and is, therefore, trapped within that medium, causing total internal reflection.

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