Optics and Telescopes Help (page 2)
Until a few hundred years ago, the only instrument available for astronomical observation was the human eye. This changed in the 1600s when several experimenters, including such notables as Galileo Galilei and Isaac Newton, combined lenses and mirrors to make distant objects look closer. Since then, optical telescopes have become larger and more sophisticated. So have the ways in which the light they gather is scrutinized.
You have learned that visible light always take the shortest path between two points and that it always travels at the same speed. These are the cornerstones of relativity theory and can be taken as axiomatic as long as the light stays in a vacuum. However, if the medium through which light passes is significantly different from a vacuum, and especially if the medium changes as the light ray travels through it, these principles of relativity do not apply.
Let’s focus our attention on what happens when light passes through a medium such as glass or is reflected by mirrors. If a ray of light passes from air into glass or from glass into air, the path of the ray is bent. Light rays change direction when they are reflected from mirrors. This has nothing to do with relativity. It happens all the time, everywhere you look. It even takes place within your own eyes.
What is a ray of light ? Definitions vary. Informally, a thin shaft of light, such as that which passes from the Sun through a pinhole in a piece of cardboard, can be called a ray or beam of light. In a more technical sense, a ray can be considered to be the path that an individual photon (light particle) follows through space, air, glass, water, or any other medium.
Light rays have properties of both particles and waves. This duality has long been a topic of interest among physicists. In some situations, the particle model or corpuscular model explains light behavior very well, and the wave model falls short. In other scenarios, the opposite is true. No one has actually seen a ray of light; all we can see are the effects produced when a ray of light strikes something. Yet there are certain things we can say about the way in which rays of light behave. These things are predictable, both qualitatively and quantitatively. When we know these facts about light, we can build high-quality instruments for observing the Cosmos at visible wavelengths.
Prehistoric people knew about reflection. It would not take an intelligent creature very long to figure out that the “phantom in the pond” actually was a reflection of himself or herself. Any smooth, shiny surface reflects some of the light that strikes it. If the surface is perfectly flat, perfectly shiny, and reflects all the light that strikes it, then any ray that encounters the surface is reflected away at the same angle at which it hits. You have heard the expression, “The angle of incidence equals the angle of reflection.” This principle, known as the law of reflection , is illustrated in Fig. 17-1. The angle of incidence and the angle of reflection are both measured relative to a normal line (also called an orthogonal or perpendicular ). In the figure, these angles are denoted q . They can range from as small as 0 degrees, where the light ray strikes at a right angle, to almost 90 degrees, a grazing angle.
If the reflective surface is not perfectly flat, then the law of reflection still applies for each ray of light striking the surface at a specific point. In such a case, the reflection is considered with respect to a flat plane passing through the point tangent to the surface at that point. When many parallel rays of light strike a curved or irregular reflective surface at many different points, each ray obeys the law of reflection, but the reflected rays do not all emerge parallel. In some cases they converge; in other cases they diverge. In still other cases the rays are scattered haphazardly.
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 .
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.
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.
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.
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.
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