![]() Such rays continue down the fiber, even following it around corners, since the angles of reflection and incidence remain large.įiber optics is one application of total internal reflection that is in wide use. Light entering a thin fiber may strike the inside surface at large or grazing angles and is completely reflected if these angles exceed the critical angle. Fiber Optics: Endoscopes to Telephonesįigure 2. A number of interesting applications of total internal reflection follow. There is no total reflection for rays going in the other direction-for example, from air to water-since the condition that the second medium must have a smaller index of refraction is not satisfied. The same calculation as made here shows that the critical angle for a ray going from water to air is 48.6º, while that from diamond to air is 24.4º, and that from flint glass to crown glass is 66.3º. Different combinations of materials have different critical angles, but any combination with n 1 > n 2 can produce total internal reflection. ![]() ![]() This will make the inside surface of the clear plastic a perfect mirror for such rays without any need for the silvering used on common mirrors. This means that any ray of light inside the plastic that strikes the surface at an angle greater than 42.2º will be totally reflected. Thus, the condition that the second medium (air) has an index of refraction less than the first (plastic) is satisfied, and the equation \theta_\\ Discussion The index of refraction for polystyrene is found to be 1.49 in Figure 2, and the index of refraction of air can be taken to be 1.00, as before. What is the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air? Strategy Note the above equation is written for a light ray that travels in medium 1 and reflects from medium 2, as shown in the figure.Įxample 1. ![]() Total internal reflection occurs for any incident angle greater than the critical angle θ c, and it can only occur when the second medium has an index of refraction less than the first. (a) A ray of light crosses a boundary where the speed of light increases and the index of refraction decreases. If the incident angle θ 1 is greater than the critical angle, as shown in Figure 1c, then all of the light is reflected back into medium 1, a condition called total internal reflection.įigure 1. That is, θ c is the incident angle for which θ 2 = 90º. The largest the angle of refraction θ 2 can be is 90º, as shown in Figure 1b.The critical angle θ c for a combination of materials is defined to be the incident angle θ 1 that produces an angle of refraction of 90 º. (Since n 1 > n 2, the angle of refraction is greater than the angle of incidence-that is, θ 1 > θ 2.) Now imagine what happens as the incident angle is increased. If, as shown in the figure, the index of refraction for the second medium is less than for the first, the ray bends away from the perpendicular. Part of the light crosses the boundary and is refracted the rest is reflected. Interestingly, we can produce total reflection using an aspect of refraction.Ĭonsider what happens when a ray of light strikes the surface between two materials, such as is shown in Figure 1a. But it would be useful to have a mirror that reflects all of the light that falls on it. Analyze the reason for the sparkle of diamonds.Ī good-quality mirror may reflect more than 90% of the light that falls on it, absorbing the rest.Describe the workings and uses of fiber optics.Explain the phenomenon of total internal reflection.By the end of this section, you will be able to:
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