Trigonometry is used in optics, the study of the behavior of light. The phenomena of most interest are reflection and refraction. A light ray changes direction when it is reflected from a mirror or smooth, shiny surface. If a ray of light passes from one transparent medium into another, the ray may be bent; this is refraction.
A clear pool looks shallower than it actually is because of refraction. This effect occurs because different media transmit light at different speeds. The speed of light is absolute and constant in a vacuum, where it travels at about 2.99792 × 10 8 meters per second. In air, the speed of light is a tiny bit slower than it is in a vacuum; in most cases the difference is not worth worrying about. But in media such as water, glass, quartz, and diamond, the speed of light is significantly slower than it is in a vacuum, and the effects are dramatic.
Index Of Refraction
The refractive index , also called the index of refraction , of a 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 m is the speed of light in medium M, then the index of refraction for medium M, call it r m , can be calculated simply:
r m = c/c m
It’s important to use the same units, such as meters per second, when expressing c and c m . According to this definition, the index of refraction of any transparent material is always larger than or equal to 1.
The higher the index of refraction for a transparent substance, the greater the extent to which a ray of light is bent when it strikes the boundary between that substance and air at some angle other than the normal. Various types of glass have different refractive indices. Quartz has a higher refractive index than any glass; diamond has a higher refractive index than quartz. The high refractive index of diamond is responsible for the “sparkle” of diamond “stones.”
Light Rays At A Boundary
A qualitative example of refraction is shown in Fig. 10-3A, when the refractive index of the first (lower) medium is higher than that of the second (upper) medium. A ray striking the boundary at a right angle (an angle of incidence of 0° relative to the normal) passes through the boundary without changing direction. But a ray that hits at some other angle is bent. The greater the angle of incidence, the sharper the turn the beam takes at the boundary.
When the angle of incidence reaches a certain critical angle , then the light ray is not refracted at the boundary, but instead is reflected back into the first medium. This is known as total internal reflection .
In air, the speed of light varies just a little bit depending on the density of the gas. Warm air tends to be less dense than cool air, and as a result, warm air has a lower refractive index than cool air. The difference in the refractive index of warm air compared with cooler air can be sufficient to produce total internal reflection if there is a sharp boundary between two air masses whose temperatures are different. This is why, on warm days, you sometimes see “false ponds” over the surfaces of blacktop highways or over stretches of desert sand. This phenomenon is also responsible for certain types of longdistance radio-wave propagation in the earth’s atmosphere. Radio waves, like visible light, are electromagnetic in nature, and they obey the rules of reflection and refraction.
Now consider what happens when the directions of the light rays are reversed. This situation is shown in Fig. 10-3B. A ray originating in the first (upper) medium and striking the boundary at a grazing angle is bent downward. This causes distortion of landscape images when viewed from underwater. You have seen this effect if you are a SCUBA diver. The sky, trees, hills, buildings, people, and everything else, can be seen within a circle of light that distorts the scene like a wide-angle lens.
If the refracting boundary is not flat, the principles shown by Fig. 10-3 still apply for each ray of light striking the boundary at any 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.
Practice problems for these concepts can be found at: Reflection and Refraction Practice Test
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