There are three features of a telescope that enable them to extend the power of our vision: a telescope's superior light-gathering ability enables us to see faint objects, a telescope's superior resolving power enables us to see even the tiniest of details, and the magnification power enables us to enlarge tiny images. Department stores and camera shops which do not know anything about telescopes, loudly proclaim their telescope's magnifying power. Magnification is the least important power of a telescope. Amateur and professional astronomers know that the light-gathering power and resolving power are the most important. These two abilities depend critically on the objective, so they make sure the optics of the objective are excellent.
The area of the objective is the determining factor. Since most telescope objectives are circular, the area = p × (diameter of objective)2/4, where the value of p is approximately 3.1416. For example: a 40-centimeter mirror has four times the light-gathering power as a 20-centimeter mirror [( p402/4) / ( p202/4) = (40/20)2 = 4].
= 252,000 × (observation
wavelength) / (objective diameter). The wavelength and
diameter must be measured in the same length units (i.e., both wavelength and
objective diameter given in meters or both in nanometers). A telescope with one arc
second resolution would be able to see a dime from about 3.7 kilometers (2.3 miles) away.
Modern telescopes are able to count the number of lines in President Roosevelt's
hair on a dime at that distance.
The desire is to make
as small as possible. This can be done by making the observation wavelength
small (e.g., use UV instead of visible light) or by making the objective diameter
large. Another way to understand it is the more waves that can be packed on the
objective, the more information the telescope detects and, therefore, the more
detailed the image is. A 40-centimeter telescope has two times the resolution of
a 20-centimeter telescope at the same observing wavelength
( for the 40-centimeter
telescope is one-half the
for
the 20-centimeter telescope). However, fluctuations in the
atmosphere will
usually smear images into a fuzzy blob about one arc second or more across so the
resolution is usually limited to the resolution from a 12.5-centimeter telescope
on the ground. I will discuss the atmosphere's effect on images further in the
next section and ways you can compensate for it.
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The desire for greater resolving power is the main reason why radio telescopes are so enormous compared to their optical counterparts. Radio wavelengths are LARGE so the radio telescope must be LARGE to get decent resolving power. The Keck 10-meter telescope is considered a very large optical telescope. However, it is easily dwarfed by the HUGE 305-meter Arecibo Radio Telescope at the Arecibo Observatory. A picture of this telescope is shown at left. This telescope was built in a natural bowl-shaped valley in Puerto Rico. Clicking on the image will show the telescope from other perspectives. |
Another way to increase the resolution is to connect telescopes together to make an interferometer. Radio waves from an object reach each telescope in the interferometer at slightly different times, so the waves are out of sync with one another. Knowing the distances between the telescopes and how out of sync the waves are, the signals can be combined electronically to create an image of exceptional resolution. The image has the same sharpness as one taken by a single instrument that would extend from one end of the interferometer to the other. The light-gathering power is equal to the sum of the light-gathering powers of each individual telescope.
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A spectacular example of such a system is the Very Large Array shown here. This telescope is made of 27 radio dishes, each 25 meters in diameter, on a Y-shaped track. Fully extended, the Very Large Array is 36 kilometers across and has a resolution of around one arc second (depending on the radio wavelength). It has the light-gathering power of a 130-meter telescope. Aerial views are shown below. |
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The Very Large Baseline Array is a huge interferometer that uses ten telescopes placed in sites from Hawaii to the Virgin Islands. This telescope is the 8,600 kilometers across and has a resolution as good as 0.0002 arc second! With a resolution about 50 times better than the Hubble Space Telescope, it is able to detect features as small as the inner solar system at the center of our galaxy, about 26,000 light years away. Astronomers are developing plans to build radio telescopes out in space to make interferometers much larger than the Earth. Astronomers are also connecting optical telescopes to increase their resolving power.
The set of four figures below shows the effect of a larger objective
size. They have the same magnification. These are
ideal images of two stars separated by 0.5
arc seconds which would be the angular separation for stars at the Sun and
Jupiter's positions if the system was 33 light years from us. The frames
are 1.5 arc seconds square and are at the observation wavelength of
500 nanometers. The resolving power is given by
and they all have the same
brightness---the light in the bottom images from the large telescopes is just
more more concentrated than for the small telescopes. The image from the 0.1524-meter
telescope (image A) would take 30
minutes to make, but the image from the 5.08-meter telescope (image D) would
take only 1.6 seconds! The exposure times for the other telescopes are given.
The pictures clearly show the increase in sharpness as the objective size is increased. The size of each of the blobs is the size of the smallest detail that can be seen with that telescope under ideal conditions. Atmospheric distortion effects (smearing of the binary star images to a blob the size of the entire frame) and obscuration and diffraction by the secondary and its supports are NOT shown here.
| interferometer | light-gathering power | magnifying power> |
|---|---|---|
| resolving power |
=
252,000×(observation wavelength/diameter of objective). Better resolving power has smaller
.
Go to
telescope introduction section
Go to
effect of our atmosphere section
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Physical Science Dept.
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Bakersfield, CA 93305-1219