Magnification = 100/4.0 = 25 (usually written as 25×)
Light travels through a vacuum at its maximum speed of about 3.0 × 108 m/s, and in a straight path. Light travels at slower speeds through different materials, such as glass or air. When traveling from one medium to another, some light will be reflected at the surface of the new medium. The light that continues through the new medium will either speed up or slow down depending on how fast it can travel through each medium. For example, light travels more quickly through air than through water. The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium. The higher the refractive index, the more light is slowed down by the substance.
|Substance||Index of Refraction|
If light enters the new medium at a right angle to the surface, it will change speed, but not direction. If it enters at an angle, its speed and its direction will change. The direction the light takes depends on whether it travels faster or slower in the new medium. Imagine driving a car from smooth pavement onto a sandy beach. If you approach the beach straight on, the car will slow down, but not change direction. If the you approach the beach at an angle, one of the tires will be slowed down by the sand before the other is, and the car will turn in the direction of the tire that touched the sand first.
Light follows the same same principle and bends towards the normal when traveling into a medium with a higher index of refraction, and away from the normal when traveling into a medium where it can go faster. In the diagram below, light is leaving air and entering glass, so it bends towards the normal on the way in, and away on the way out of the glass.
Diagram showing how light changes direction as it moves into and out of a medium with a higher index of refraction. Credit: LCO
Lenses form images by refraction and are typically made of either glass or plastic. They are ground so that their surfaces are either segments of spheres or planes. If a lens is convex or converging, it takes parallel light rays from a distant object and bends them so that they converge to a single point called the focal point. The distance from the lens to the focal point is called the focal length of the lens.
Diagram of a convex lens, showing how the light is refracted and converges to a focal point.
If a lens is concave or diverging, it takes parallel rays and bends them so that they spread out. The rays will then appear to originate from a point in front of the lens. This point is also called the focal point, and its distance is measured in negative units.
The earliest telescopes, as well as many amateur telescopes today, use lenses to gather more light than the human eye could collect on its own. They focus the light and make distant objects appear brighter, clearer and magnified. This type of telescope is called a refracting telescope.
Most refracting telescopes use two main lenses. The largest lens is called the objective lens, and the smaller lens used for viewing is called the eyepiece lens.
Diagram of what happens to light in a refracting telescope.
Eight-Inch refracting telescope. Image credit: Chabot Space and Science Center
The size of an image produced by a lens is proportional to the focal length of the lens. The longer the focal length, the larger the image. The brightness of an image from a telescope depends partly on how much light is collected by the telescope. The light-gathering power of a telescope is directly proportional to the area of the objective lens. The larger the lens, the more light the telescope can gather. Doubling the diameter of the lens increases the light gathering power by a factor of 4. Brightness of images also depends on how big an area the image light is spread over. The smaller the area, the brighter the image.
The magnifying power of a telescope is the ratio of an object's angular diameter to its naked eye diameter. This depends on the focal length of both lenses.
Magnification = focal length of objective lens / focal length of eyepiece lens
Magnification might seem like the most important aspect of a telescope, but there are limits to how sharp an image a telescope can produce because of the blurring effects of the Earth's atmosphere. Magnifying a blurred image makes it bigger, but not clearer, so the priority when telescopes are built is to have the greatest light-gathering power possible. Gathering more light makes brighter images, and brighter images make it easier to see faint details.
Galileo is credited with being the first person to use a telescope to make observations of the night sky. After hearing of the invention of the telescope in 1608, he built one of his own, called a Galilean Telescope, in 1609 using a convex objective lens and a concave eyepiece lens. His telescope could magnify objects 3 times. Telescopes he made later magnified objects up to 30 times.
Diagram of the path light travels in a Galilean telescope. Credit: LCO
Lenses create a type of image distortion known as chromatic aberration. This occurs because as light passes through a lens, different colors are bent through different angles (like in a prism) and brought to a focus at different points. Because of this, stars viewed through a simple lens are surrounded by rainbow colored halos. This can be corrected for by adding a thin lens of a different kind of glass behind the objective lens.
Lenses present other optical problems including how difficult and expensive it is to make large lenses completely free of defects. Glass also absorbs most ultraviolet light, and visible light is substantially dimmed as it passes through a lens. In addition, lenses in telescopes can only be supported around the outside, so large lenses can sag and distort under their own weight. All of these problems affect image quality and clarity.
A small refracting telescope has an objective of focal length 100 cm. If the eyepiece has a focal length of 4.0 cm, what is the magnification of the telescope?