Is it possible to have total internal reflection for light

This angle of incidence is called the critical angle. The critical angle varies for different materials, but it is useful to know that it is around 42 degrees for glass. You will be reminded of this fact in the exam. The diagram below shows light hitting the glass-air boundary at an angle that is equal to the critical angle.

But it would be useful to have a mirror that reflects all of the light that falls on it. Interestingly, we can produce total reflection using an aspect of refraction. Consider what happens when a ray of light strikes the surface between two materials, such as is shown in Figure 1a. Part of the light crosses the boundary and is refracted; the rest is reflected. 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.

Now imagine what happens as the incident angle is increased. Figure 1. The ray bends away from the perpendicular. 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.

What is the critical angle for light traveling in a polystyrene a type of plastic pipe surrounded by air? The index of refraction for polystyrene is found to be 1. This means that any ray of light inside the plastic that strikes the surface at an angle greater than 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. The same calculation as made here shows that the critical angle for a ray going from water to air is 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.

A number of interesting applications of total internal reflection follow. Figure 2. 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. Such rays continue down the fiber, even following it around corners, since the angles of reflection and incidence remain large. Fiber optics is one application of total internal reflection that is in wide use. In communications, it is used to transmit telephone, internet, and cable TV signals.

Fiber optics employs the transmission of light down fibers of plastic or glass. Because the fibers are thin, light entering one is likely to strike the inside surface at an angle greater than the critical angle and, thus, be totally reflected See Figure 2. The index of refraction outside the fiber must be smaller than inside, a condition that is easily satisfied by coating the outside of the fiber with a material having an appropriate refractive index.

In fact, most fibers have a varying refractive index to allow more light to be guided along the fiber through total internal refraction. Rays are reflected around corners as shown, making the fibers into tiny light pipes. Figure 3. Bundles of fibers can be used to transmit an image without a lens, as illustrated in Figure 3.

The output of a device called an endoscope is shown in Figure 3b. Endoscopes are used to explore the body through various orifices or minor incisions. Light is transmitted down one fiber bundle to illuminate internal parts, and the reflected light is transmitted back out through another to be observed. Surgery can be performed, such as arthroscopic surgery on the knee joint, employing cutting tools attached to and observed with the endoscope.

Samples can also be obtained, such as by lassoing an intestinal polyp for external examination. Figure 4. Fibers in bundles are clad by a material that has a lower index of refraction than the core to ensure total internal reflection, even when fibers are in contact with one another.

This shows a single fiber with its cladding. Fiber optics has revolutionized surgical techniques and observations within the body. There are a host of medical diagnostic and therapeutic uses.

The flexibility of the fiber optic bundle allows it to navigate around difficult and small regions in the body, such as the intestines, the heart, blood vessels, and joints. Transmission of an intense laser beam to burn away obstructing plaques in major arteries as well as delivering light to activate chemotherapy drugs are becoming commonplace.

Fibers in bundles are surrounded by a cladding material that has a lower index of refraction than the core. See Figure 4. For the diamond-air boundary, the critical angle is For the diamond-water boundary, the critical angle is The critical angle is different for different media. In the next part of Lesson 3 , we will investigate how to determine the critical angle for any two materials.

For now, let's internalize the idea that TIR can only occur if the angle of incidence is greater than the critical angle for the particular combination of materials.

Total internal reflection is often demonstrated in a Physics class through a variety of demonstrations. In one such demonstration, a beam of laser light is directed into a coiled plastic thing-a-ma jig. The plastic served as a light pipe , directing the light through the coils until it finally exits out the opposite end.

Once the light entered the plastic, it was in the more dense medium. Every time the light approached the plastic-air boundary, it is approaching at angles greater than the critical angle. The two conditions necessary for TIR are met, and all of the incident light at the plastic-air boundary stays internal to the plastic and undergoes reflection.

And with the room lights off, every student becomes quickly aware of the ancient truth that Physics is better than drugs. This demonstration helps to illustrate the principle by which optical fibers work. The use of a long strand of plastic or other material such as glass to pipe light from one end of the medium to the other is the basis for modern day use of optical fibers. Optical fibers are used in communication systems and micro-surgeries.

Since total internal reflection takes place within the fibers, no incident energy is ever lost due to the transmission of light across the boundary. The intensity of the signal remains constant. Another common Physics demonstration involves the use of a large jug filled with water and a laser beam. The jug has a pea-sized hole drilled in its side such that when the cork is removed from the top of the jug, water begins to stream out the jug's side.

The beam of laser light is then directed into the jug from the opposite side of the hole, through the water and into the falling stream. The laser light exits the jug through the hole but is still in the water.

As the stream of water begins to fall as a projectile along a parabolic path to the ground, the laser light becomes trapped within the water due to total internal reflection. Being in the more dense medium water and heading towards a boundary with a less dense medium air , and being at angles of incidence greater than the critical angle, the light never leaves the stream of water.

In fact, the stream of water acts as a light pipe to pipe the laser beam along its trajectory. Once more, students viewing the demonstration are convinced of the fact that Physics is better than drugs.

For each combination of media, which light ray A or B will undergo total internal reflection if the incident angle is gradually increased? Physics Tutorial. My Cart Subscription Selection. Student Extras.