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The Telescope

A telescope is an instrument that produces a distinct, generally magnified image of a distant object by modifying its light rays with a system of lenses or mirrors.

Telescopes consist of two lenses - a lens with a large focal length turned to the object (the objective) and a lens with a small focal length that is turned to the viewer (the eyepiece). There are two types of telescopes:

- Astronomical telescope produces an inverted image of distant objects, and is therefore inconvenient for observing earthen objects. The ocular of such telescope is a converging lens.

- Galilean telescope is designed for observing earthen objects. Such telescopes produce an erect magnified image of a distant object. The ocular in a Galilean telescope is a diverging lens.

There are many different kinds of telescopes: optical telescopes (general astrophysical telescopes, coronagraphs, satellite observation telescopes), radio telescopes, infrared, neutrino, and X-Ray telescopes. Despite this variety, all telescopes that receive electromagnetic radiation have two principal tasks to accomplish:

  • To create a maximally sharp image, and to increase the angular distances between the objects of observation (stars, galaxies, etc.)
  • To collect as much radiation energy as possible, and to increase the brightness of observed objects.
The operational principles of a telescope are as follows. Parallel rays of light (e.g., rays coming from a star) fall on the objective (a mirror or a lens). The objective creates an image in the focal plane. Light rays that are parallel to the main optical axis are gathered at the focus point F, which lies on this axis. Other beams of light are gathered in the vicinity of the focus, either above or below it. An observer sees the resulting image with an eyepiece.

The diameters of the input and output beams are considerably different (the input beam has an objective diameter, whereas the output beam has the diameter of an objective image created by the eyepiece). At the point when the light gathered by the objective penetrates the observer's pupil, the gain is proportionate to a square of the ratio between the objective and the pupil. In large telescopes, this value accounts for the magnification of the image by tens of thousands of times.

A telescope's ability to increase the angle is characterized by the telescopic magnification. Magnification is equal to the ratio of focal distances of objective F and eyepiece f.

Γ = F

When analyzing the properties of rays in a telescope, it is usually assumed that the viewer's eye is accommodated at infinity. This is why the rays are parallel upon their exit from the telescope. Such a condition is achieved when the distance between the objective and the eyepiece equals to the sum of their focal lengths f1+f2.

When an object (and its image) is at infinity, it is senseless to consider lateral magnification. Telescopes are characterized by angular magnification M that is defined as the ratio of the angle θ subtended at the eye by the final image to the angle θ subtended at the unaided eye by the object (for small angles). Angles θ and θ' are the angles between the optic axis of the system and the parallel rays from a point on an object or its image. It is convenient to think of these angles as bearing negative or positive signs, so that the sign of angular magnification M would represent the type of the image (erect or inverted).

Magnification can be easily expressed by a formula that utilizes the focal lengths of the objective and the eyepiece:

M = θ' =   f1
θ f2

Select a binary star as your object of observation in the model's top window. Following the selection, the window will display the interference pattern that is visible while making observations with a high-resolution telescope. Note that the resolution changes when the diameter of the objective is modified.

Switch to Diagram regime. Observe the dependence of radiation intensity in the telescope's focal plane on the distance to center. Each component of the binary star contributes to the total intensity.

Study the diagram of a refracting telescope. The lower windows display the experiment parameters: distance to the object, diameter and focal distance of the objective, and the telescope's angular resolution. Press "Reset" button to select a new binary star for observation.

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