7.3.1: Illustrations

Illustration 1: Huygens' Principle and Refraction

Huygens' principle states that all points on a wave front serve as point sources for secondary spherical waves that propagate outward. The position of the wave front at some later time is determined by the tangent to the surface of the secondary wave fronts. Huygens' principle can be used to predict observed optical phenomena such as refraction. Although the principle may seem strange and contrived, it is a direct consequence of the differential wave equation. This Illustration shows you Huygens' principle applied to light passing between two mediums. Restart.

The animation begins with the n₁ = n₂ animation. Click "play" to begin. You will see a wave front, represented by a white line, moving at an angle across the screen. Huygens' principle applies to all points along the path of the wave front. However, to make it simple, the visualization of the creation of the secondary wave fronts is only shown for the points down the center of the applet. In this case the medium on the right and left of the points is the same. As the applet plays, carefully watch as the secondary wave fronts are formed at the points in the center. Notice how the wave front, now defined as the tangent to the surface of the secondary wave fronts, is exactly the same as it was before. View the n₁ = n₂ animation several times until you feel comfortable with what it represents.

Now initialize and play the n₂ > n₁ animation. In this animation, the wave front passes from one medium to another. Because n₂ > n₁, the waves slow down in the second medium. Carefully watch as the wave front passes from one medium to another. Since the wave fronts are traveling slower in the second medium, you see the primary wave front bend downward. This is particularly apparent if you pause the applet just as the wave front reaches the medium and then step forward as the wave front passes into the new medium.

Finally, initialize and play the n₂ < n₁ animation. In this case the waves speed up in the second medium and you see the wave front bend upward.

Illustration authored by Melissa Dancy.
Script authored by Morton Brydensholt.

Illustration 2: Fiber Optics

When you carry on a telephone conversation or watch cable television you are likely utilizing fiber optic technology to transmit and receive information. A fiber optic cable provides a less expensive, higher capacity alternative to copper wire with less signal degradation. You may think of fiber optics as being high tech, but the physics behind it is actually quite simple. Restart.

When light is incident on a medium of lower index of refraction at an angle greater than the critical angle, all of the light will be reflected. In the animation, a source of parallel rays of light is embedded in a medium of higher index of refraction than its surroundings. When the animation begins, the light rays strike the interface at an angle less than the critical angle for these two substances. Adjust the angle of the rays by clicking on the beam and then click-dragging the hotspot. At some point the angle is increased beyond the critical angle and the rays are entirely reflected back into the medium.

A fiber optic cable is a thin strand of glass surrounded by a material with an index of refraction less than glass. Light will travel through a fiber optic cable just as the light in the animation was transmitted through the blue region by reflecting off the boundary between the two materials.

Illustration authored by Melissa Dancy.

Illustration 3: Prisms and Dispersion

The index of refraction of a given material depends on the wavelength (or frequency) of the incoming light. Hence, the speed of light in that material also depends on the wavelength or frequency of light. Restart.

When the index of refraction of a material is given, therefore, it is really true for only one particular wavelength or color of light. This slight variation in the index of refraction leads to what are called chromatic aberrations in lenses (where the focal point is different for different colors). It is what allows for the separation of white light into colors using a prism (or drops of water). This phenomenon is called dispersion. When the speed of a wave in a particular medium is a function of frequency, the medium is dispersive. Note that for this Illustration we consider the dispersive qualities of glass (\(1.6 < n < 1.68\)), but air itself is also dispersive (\(1.45 < n < 1.47\)).

Change the wavelength of light (in air) and therefore change the color of the light entering the prism. Notice the angle at which the different colors exit the prism and the different index of refraction associated with each color.

When white light enters the prism, what happens? This is a very nice example of dispersion in glass. You see a rainbow of colors, both inside and outside of the prism, because each light ray refracts differently depending on its wavelength (or frequency). A raindrop can also refract sunlight. The result of the dispersion of light in water droplets during a passing rainstorm is often a rainbow.

Illustration authored by Morten Brydensholt and Anne J. Cox.
Script authored by Morten Brydensholt.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.