Refracting telescope

The second negative lens is positioned so that its second focal point is exactly coincident with the second focal point of the objective lens. Thus the rays that are aimed at producing the real, inverted image shown above, actually hit the second lens before they get to the image.

To construct the image produced by the second lens, keeping in mind that the top ray in the figure above, which was headed for the focal point of the 1st lens, is also headed for the same focal point of the 2nd lens. This ray is refracted parallel to the axis, and this is shown in red. How does this then make the image appear?

The Galilean telescope         The objective lens, whose focal length is f, performs the same function as in a Keplerian telescope: acting alone, it would form a real, inverted image of the distant object, as shown in the diagram ->

Galilean Telescope

Keplerian Telescope

Galilean: The negative eyepiece intercepts the converging rays coming from the objective, rendering them parallel and thus forming, to the infinite (afocal position), a virtual image, magnified and erect.

Keplerian: The objective forms a real image, diminished in size and upside-down, of the object observed. The eyepiece — consisting of a converging lens with short focal length, is actually a magnifying lens — enlarges the image formed by the objective.

Newtonian Reflector

The eye lens not only converts the cones of light into parallel pencils, it also bends the angles of the central rays so they diverge more rapidly than when they entered the lens. The factor by which the angle of divergence increases is the ratio F/f, which is the magnification of the telescope.

The Hubble Space Telescope's angular resolution = 0.05 arcseconds

5/100ths of 1/3600 of a degree

The human eye's angular resolution = 1 arcminute (1/60 of a degree)

Diffraction ( Rayleigh) limit Light waves spread out when they go through holes (lenses) "diffraction limit" = 2.5 x 105 arcsec * wavelen./diameter

The resolution of a telescope refers to the true (as opposed to magnified) angle between the most closely spaced features it can separate. The maximum resolution achievable by any telescope is limited by a phenomenon called diffraction -- the spreading out of light due to its wave nature. A point of light is actually focused into a central spot surrounded by a faint pattern of rings, as can be seen in this picture. For light of a single color, the width of the diffraction pattern is directly proportional to the wavelength and inversely proportional to the aperture (diameter of the front opening) of the telescope. The usual figure quoted for the ultimate resolution is based on a standard proposed by Lord Rayleigh in 1879 and refers to the minimum spacing at which two equal points of light can be distinguished. For a wavelength in the middle of the visible band (mercury green line = 5461 Å) and an aperture of 1 inch (25.4 mm) the Rayleigh limit is 5.41 arc-seconds.

As indicated above, the diameter of this spot will decrease as the diameter of the objective lens is increased. Images of extended sources (such as a planet or a two-dimensional test target) suffer from diffractive blurring just as much as do those from point sources, because in truth the image of an extended source is nothing more than the sum of the diffraction patterns from each individual point in that source.

For a telescope the theoretical intrinsic minimum angular separation is given byamin = 1.22 l/D

where l is the wavelength of the light D the diameter of the objective.

For the human eye and visible light D = 0.8 cm and l = 500 nm,

therefore amin = 7.62 10-5 rad = 4.37 10-3 degree.