## Refracting telescopes

In a refracting telescope, the light first passes through a large lens, called the objective lens. The objective is the part that intercepts the incoming light, so it determines the light-gathering power of the telescope. The larger the objective is, the greater the light-gathering power. The light passing through the objective is concentrated on a second lens, called the eyepiece. The eyepiece is used to inspect the image formed by the objective. The image formed by the eyepiece is viewed either by the eye or by a camera. In practice, either the objective or the eyepiece may be a multiple lens, to correct for aberrations, but we will treat each as a single optical element. It is also possible to just have a film holder with no camera lens.

Objective

Objective

9 Image formation in a refracting telescope. Light from a star enters from the left, making an angle 0 with the axis, and leaves the eyepiece making a larger angle q> with the axis.The focal lengths of the objective, eyepiece and camera lens are indicated. For each lens, the ray that goes through the center undeflected (the chief ray) is indicated as a heavier line. In a real telescope, the angles would be much smaller.

9 Image formation in a refracting telescope. Light from a star enters from the left, making an angle 0 with the axis, and leaves the eyepiece making a larger angle q> with the axis.The focal lengths of the objective, eyepiece and camera lens are indicated. For each lens, the ray that goes through the center undeflected (the chief ray) is indicated as a heavier line. In a real telescope, the angles would be much smaller.

The basic arrangement of the refracting telescope is shown in Fig. 4.5. We follow the formation of the images of two stars, just as we did with the camera. Let's assume that the focal length of the objective is fobj. Since the stars are at infinity, the objective forms their images this distance behind the objective. The eyepiece has a focal length feye. We place the eyepiece this distance behind the images formed by the objective. (This means that the objective and eyepiece are separated by a distance equal to the sum of their focal lengths.) Since the initial images of the stars are feye from the eyepiece, the eyepiece will focus the light at infinity. This means that all of the rays in a given bundle emerge from the eyepiece parallel to one another.

If you now look through the eyepiece, and focus your eyes at infinity (by relaxing the muscles around your eye), the rays in each bundle will be brought back together on your retina. Similarly, if you use a camera, you focus the camera at infinity, and the images of the stars will fall on the film. The need to focus your eyes at infinity means that the best way to look through the eyepiece is to relax both eyes and cover the unused eye, rather than squinting to close the unused eye.

Lets's go back to the two bundles of rays emerging from the eyepiece. Even though the rays within a given bundle are parallel to one another, the bundles make some angle with each other. If the two stars are an angle 0 apart on the sky, then the two bundles will enter the objective, making this angle with each other. The bundles leave the eyepiece, making a larger angle 9 with each other. We can find the angle 9 by following the chief ray through the eyepiece. Note that the chief ray at the eyepiece is not the same ray that was the chief ray at the objective. However, all rays in a given bundle will emerge from the eyepiece parallel to the new chief ray.

From the two right triangles in the diagram with the common side x, we see that tan 0 = x/fobj tan p = x/feye

If the angles are small, we can replace the tangent of the angle with the value of the angle in radians. If we also eliminate x in the equations, we find p/0

fobj//eye

This means that we have an angular magnification equal to the ratio of the value of the focal lengths of the two optical elements.

In general, when we want to do work with good detail in the image, we use a telescope with a long focal length objective. Of course, we can change the angular magnification of a telescope by changing the eyepiece. There is a practical limit. You don't want to magnify the image so much that you blow up the blurring caused by atmospheric seeing.

There are some limitations in the use of a refracting telescope. One problem is the chromatic aberration of the objective. Also, the objective must be made from a piece of glass that is perfect throughout its volume, since the light must pass through it. This is harder as you try to make larger objectives. Larger objectives are also harder to support. The objective can only be supported at its edges, since light must pass through. Also, in many modern applications, we want to place instruments near the eyepiece. However, the telescope must be supported closer to the center of mass, which means far from the eyepiece. Any instrument hung at the eyepiece will exert a large torque about the mount, limiting the weight of the instrument. As a practical matter, the largest refractors, such as that shown in Fig. 4.6, have objectives with diameters of, at most, 1 m.

(4.3) 4.3 I Reflecting telescopes

Many of the difficulties with refracting telescopes are avoided with reflecting telescopes. In reflectors, the objective lens is replaced by an objective mirror. With a mirror, there is no problem of chromatic aberration, since light of all wavelengths is

The 1 m refracting telescope at the Yerkes Observatory. Note the long distance over which the observer must move to keep up with the eyepiece. [Yerkes Observatory photograph]

The 1 m refracting telescope at the Yerkes Observatory. Note the long distance over which the observer must move to keep up with the eyepiece. [Yerkes Observatory photograph]

(a) The 5 m diameter Hale telescope on Mt Palomar (California). For almost four decades it was the largest useful telescope in the world.The caged part is the telescope. It has an equatorial mount.The solid piece in the foreground is part of the fork shaped support for the telescope.To track an object, as the Earth rotates, the whole fork rotates in the opposite direction.The prime focus cage is near the top of the telescope. (b) The 4 m diameter Mayall telescope of the National Optical Astronomy Observatory, on Kitt Peak, Arizona.There is an identical telescope located on Cerro Tololo, Chile.The Cassegrain focus is in a cage below the tele-scope.The observer does not stay in that cage for observing; that is done from a control room, where a television is used to keep track of where the telescope is pointing. [(a) Palomar Observatory/California Institute of Technology; (b) NOAO/AURA/NSF]

reflected at the same angle. The mirrors are made by shaping and then polishing a large piece of glass. While the polished surface has some reflective ability, it is not enough for a good mirror. Therefore a thin layer of reflecting material (usually aluminum) is deposited on the surface. The process of applying the reflective coating is called aluminization. This is best done under very clean conditions and under close to vacuum conditions, to avoid impurities on the surface. The chamber in which this is done is called an aluminization chamber. Typically the effects of dust and oxidation result in telescopes needing a new coating every few years. So, large telescopes generally have aluminizing chambers near the telescope.

Since the light doesn't pass through the glass, the requirements are for a good surface, not a good volume. Moreover, the glass can be supported from behind. It is therefore possible to make reflectors larger than refractors. For many years the largest reflector was the 5 m (200 inch) diameter Hale telescope on Palomar Mountain (Fig. 4.7a).

One advantage of the wave nature of electromagnetic radiation is that the radiation is essentially unaffected by objects much smaller than the wavelength. When electromagnetic waves reflect off a metal surface, they do it by inducing an oscillating current in the surface. This oscillating current then produces the reflected wave. If the surface is much smaller than the wavelength, there will not be enough room to produce a reflected wave at this wavelength. This means that to have good image formation, the surface of the mirror must be perfect to within approximately A/20, where A is the wavelength of the light being observed. For example, if you are observing with a wavelength of 500 nm, the surface must be accurate to within 25 nm. (This is about 250 atoms.)

Various shapes are possible for the mirror. It turns out that spherical ones are the easiest to grind. You may remember that a parabola focuses to a single point all rays coming in parallel to the axis. This means that a paraboloid, where any cross section of the mirror will be a parabola, is a useful shape. Paraboloids are generally easy to grind, if you start with a spherical shape and then make a slight adjustment (taking a little glass off the center). Current grinding technologies (discussed below) allow customized shaping of the mirror to optimize for various applications (e.g. better imaging over a wide field).

We now look at what happens to the image formed by the objective. Replacing the lens with a mirror doesn't change any of the basic ideas of image formation. There is, however, a problem caused by the reflection of the light back along the direction from which it came. To examine the image, the eyepiece (and observer) must be placed between the stars and the mirror, blocking some of the incoming light. If an eyepiece is put at this location, we call the arrangement a prime focus. The advantage of the prime focus is that no more mirrors are required, so light is not lost (or images distorted) in additional reflections. It provides for a 'fast' system (small focal ratio) with a large field of view. However, there is some blockage of the objective. If the telescope is very large, this blockage is a small fraction of the total collecting area of the objective.

Example 4.3 Blockage in prime focus Consider a 5.0 m diameter telescope, with a 1.0 m diameter prime focus cage. What fraction of the incoming light is blocked by the cage?

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