Optics and Telescopes Help

Refraction

Prehistoric people noticed refraction as well as reflection; a clear pond looks shallower than it actually is because of this effect. People who used spears to catch fish learned to compensate for the effects of refraction; the images of fish were displaced more or less depending on the angle at which they were observed. The cause and the far-reaching uses of visible-light refraction were not known or understood until quite recently. There is evidence that ancient Greeks and Romans knew how to make crude lenses for the purpose of focusing light beams, but more refined applications apparently evaded them.

When light rays cross a flat boundary from one clear medium into another having different light-transmission properties, the rays are bent, or refracted . An example is shown in Fig. 17-2 when the refractive index of the initial medium, called medium X in the figure, is higher than that of the final medium, called Y . (The refractive index, also called the index of refraction , is defined in the next section.) A ray striking the boundary at a right angle passes through without changing direction. However, a ray that hits at some other angle is bent; the greater the angle of incidence, the sharper is the turn. When the angle of incidence reaches a critical angle , then the light ray is not refracted at the boundary but is reflected back into medium X . This is total internal reflection .

Figure 17-2. Rays of light are bent more or less as they cross a boundary between media having different properties.

If the directions of the light rays in Fig. 17-2 are reversed, they still follow the same paths. Thus a ray originating in medium Y and striking the boundary at a grazing angle is bent downward at a considerable angle. This causes significant distortion of images when viewed from underwater. You have surely seen this effect if you are a scuba diver. The entire landscape above the water looks as if it is viewed through a wide-angle lens.

If the refracting boundary is not perfectly flat, then the principle shown by Fig. 17-2 still applies for each ray of light striking the boundary at a specific point. The refraction is considered with respect to a flat plane passing through the point tangent to the boundary at that point. When many parallel rays of light strike a curved or irregular refractive boundary at many different points, each ray obeys the same principle individually. As a whole, however, the effect can be much different than is the case for a flat boundary. In some cases parallel rays converge after crossing the boundary; in other cases they diverge. In still other cases the rays are scattered.

Refractive Index

Different media transmit light at different speeds. This does not violate the fundamental principle of relativity theory. The speed of light is absolute in a vacuum, where it travels at 299,792 km/s or 186,282 mi/s expressed to six significant digits. However, light travels more slowly than this in other media because the relativistic principle only applies for a vacuum.

In air, the difference in the speed of light is slight, although it can be significant enough to produce refractive effects at near-grazing angles between air masses having different densities. In water, glass, quartz, diamond, and other transparent media, light travels quite a lot more slowly than it does in a vacuum. The refractive index of a particular medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. If c is the speed of light in a vacuum and c _x is the speed of light in medium X , then the index of refraction for medium X , call it r _x , can be calculated simply:

r _x = c / c _x

Always use the same units when expressing c and c _x . According to this definition, the index of refraction of any transparent material is always greater than or equal to 1.

The greater the index of refraction for a transparent substance, the more a ray of light is bent when it passes the boundary between that substance and air. Different types of glass have different refractive indices. Quartz refracts more than glass, and diamond refracts more than quartz. The high refractive index of diamond is responsible for the multicolored shine of diamond stones.

Dispersion

The index of refraction for a particular substance depends on the wavelength of the light passing through it. Glass slows down light the most at the shortest wavelengths (blue and violet) and the least at the longest wavelengths (red and orange). This variation of the refractive index with wavelength is known as dispersion . It is the principle by which a prism works (Fig. 17-3). The more the light is slowed down by the glass, the more its path is deflected when it passes through the prism. This is why prisms cast rainbows when white light shines through them.

Figure 17-3. Dispersion is responsible for the fact that a glass prism “splits” white light into its constituent colors.

Dispersion is important in optical astronomy for two reasons. First, a prism can be used to make a spectrometer , which is a device for examining the intensity of visible light at specific wavelengths. (Gratings are also used for this.) Second, dispersion degrades the quality of white-light images viewed through lenses unless those lenses are specially made to cancel out the effect.

Practice problems of this concept can be found at: Optics and Telescopes Practice Problems