eyepiece. The original is on the
right.A Galilean telescope is an unusual instrument. It has a concave
lens for an eyepiece. The original is on the
right.
A ray diagram for a Galilean telescope is awkward to draw. The small inverted real image formed by the objective forms a virtual object close to the focal length of the concave eyepiece. When the object is very far away, (for most comfortable viewing), the real image is at the focal length of the eyepiece and the final upright virtual image is formed at infinity.
The magnification of the telescope is then given simply by ...
Galilean telescopes of low magnification can be made very short. We still use them for opera glasses, where small size is more important than other considerations.
Galileo's original self-made telescope was about a meter long and 2 cm in diameter. A year before Galileo died in 1642 he was visited by Toricelli who discussed lenses among other things. Toricelli went on the make better lenses. The one shown here is a large plano-convex lens of reasonable quality, preserved in the Physics Museum in Naples.
| For the 'home-made' construction of a Galilean telescope click here. |
The binoculars shown half natural size belonged for many years to the Editor's grandfather, John Jones. Jack was a plowman with a team of four-in-hand (horses), the 1919 NZ clay-bird shooting champion, and an avid duck shooter. John's binoculars were British army issue and went through the Indian Mutiny in the 1850's. They are Galilean binoculars with just two lenses per barrel, and no prisms. They have (compared to modern binoculars of the same physical size) relatively low magnification and a small field of view.
A large convex objective of long focal length, and a short focal length convex eyepiece, are combined to form a final enlarged image.
The objective forms a real image which is then magnified by the eyepiece. When the object is very far away the focal length of the eyepiece is at the focal length of objective and the final image is at infinity; inverted, which is inconvenient for watching the neighbors; hence the name 'astronomical' telescope.
The magnification is given by ...
Refracting telescopes of large magnification must be quite long. The largest ever built is the Yerkes 40 inch monstrosity, at the University of Chicago, completed on May 20, 1897. Details at ...
http://astro.uchicago.edu/yerkes/
| For an example of a 'home-made' astronomical telescope click here. |
Inserting an erecting lens fixes the image inversion problem but it lengthens the telescope further by 4fc. It also introduces more glass surfaces which each reject about 4% of the available light. The second problem is largely eliminated by blooming the lenses with MgF2 and the length problem is solved by buying a bigger case.
| For an example of image erection for a 'home-made' astronomical telescope click here. |
Most modern refracting telescopes come in pairs.
 The optical path is folded and the images are inverted with pairs of right angled prisms. The prisms shift the optical paths inwards so the barrels can be more widely separated than the eyes. |
About 4% of light at normal incidence is returned from each surface of a glass lens (n =1.50) in air. Coating a lens with a layer of magnesium fluoride (n =1.32) one quarter of a wavelength thick, suppresses the reflection since both upper and lower MgF2 interfaces are closed boundaries and the path difference between the upper and lower reflections is one half wavelength. Zero reflection is not possible for all wavelengths in the visible spectrum. Reflection from a coated lens has a color determined by the exact thickness of the MgF2 layer.
A coated lens is said to be 'bloomed' because the appearance of the surface in reflected light is similar to the bloom on ripe fruit (plums, grapes, etc) due to an oil layer on the skin.
Isaac Newton made a mistake. He made many, as we all do, but this celebrated mistake is well known and worth remembering.
Newton made measurements of angles as he refracted light through prisms of different types of glass and concluded, (wrongly), that dispersion was proportional to refractive index. That being the case, chromatic aberration - the colored fringes seen around images which are due to dispersion - could not be corrected for. Because he thought that it was impossible to make a lens that was corrected for chromatic aberration he sought another solution.
Newton invented, and made himself, a reflecting telescope which avoided most of the chromatic aberration and made him famous. Reflecting telescopes all have a large mirror to collect light.
| For an example of a crude home-made Newtonian telescope click here. |
Reflecting telescopes come in many shapes and sizes from the humble back yard type to the gigantic professional status symbol.
All large instruments are reflecting telescopes because it is easier to make and support a large slightly nonspherical mirror, than it is to fashion and support a very large nonspherical convex lens.
Note: modern eyepieces are made from chromatic doublets - lenses corrected at one wavelength for chromatic aberration.
Good ideas sometimes take a long time to emerge. This one surfaced around 2004. Reflecting binoculars (below) allow astronomical observation with both eyes.
A clever idea but not cheap - try "reverse binoculars" on the web.
For very large telescopes the placement of the eyepiece near the aperture is inconvenient. There are several slight Newton's original design, including....
Cassegranian telescope:
A Cassegranian telescope has a central mirror to return the light from the main mirror to an eyepiece or camera on the optical axis. The main mirror is parabolic and the secondary mirror is hyperbolic. All large instruments are Cassegranian. The Hubble Space Telescope is the most sophisticated and most expensive Cassegranian ever built.
Schmidt camera:
A Schmidt camera is a Cassegranian telescope. The spherical aberration of a very short focal length spherical mirror is largely eliminated by making the film plate curved to match the curved focal plane of the mirror and a corrector plate, a very thin zero-power aspheric lens, is placed at the radius of curvature of the primary mirror. This lens is slightly convex at the center and slightly concave at the edge. Light rays at the center of the aperture are converged, those halfway out from the center are unaffected, while the light rays at the edge of the aperture are diverged. Rays are now all reflected to the focal plane by the spherical mirror.
Cerenkov telescope:
When a single very high energy cosmic ray (proton) or gamma ray (photon) enters the atmosphere, it creates a shower of relativistic electrons traveling faster than the speed of light in air. A faint blue glow of Cerenkov radiation accompanies the shower on its way to the ground. The Cerenkov radiation that accompanies the shower is a patch some 200 meters across and a few meters thick that can be detected with an array of mirrors with a sensitive detector in the focal plane. TeV (1012 eV) protons and gamma ray events can be distinguished because they each have a different light 'signature'. A gamma ray shower is recorded as a relatively narrow streak of light, and a proton event is imaged as a more diffuse patch.
The Hubble telescope is a Cassegranian design with a camera at the focal point and a 2.4 meter mirror. It is capable of imaging 30th magnitude stars. Even in space the resolution of a telescope is limited by the diffraction pattern of the aperture. The image of a star is not a point but a set of concentric rings.
Note: a close orbiting binary is said to be just resolved [by Rayleigh's criterion] if the center of one diffraction pattern coincides with the first dark fringe of the other.
The image is a diffraction pattern formed by the telescope aperture. The larger the aperture, the smaller the pattern. We need large telescopes for high resolution.
Zerodur® is a carefully chosen combination of glass with a positive expansion coefficient and a form of quartz with a negative expansion coefficient. The mixture has a near zero coefficient of thermal expansion. Due to very little transmission near the blue end of the visible spectrum Zerodur® is rarely used for lenses or prisms but it is an ideal backing for a large parabolic mirror.
Remarkable progress has been made in recent years by subtracting the effects of atmospheric turbulence to achieve better images from ground based telescopes and by linking telescopes together to increase the effective aperture. Very large arrays of radio telescopes have been built. The interested reader should consult the web for up to date information.