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Image a is a photograph one of the antennas from the Australia Telescope Compact Array. Image b is a cutaway diagram showing 4 nested sets of hard x-ray mirrors of the Chandra X-ray observatory.
(a) The Australia Telescope Compact Array at Narrabri (500 km NW of Sydney). (credit: Ian Bailey) (b) The focusing of x rays on the Chandra Observatory, a satellite orbiting earth. X rays ricochet off 4 pairs of mirrors forming a barrelled pathway leading to the focus point. (credit: NASA)

A current exciting development is a collaborative effort involving 17 countries to construct a Square Kilometre Array (SKA) of telescopes capable of covering from 80 MHz to 2 GHz. The initial stage of the project is the construction of the Australian Square Kilometre Array Pathfinder in Western Australia (see [link] ). The project will use cutting-edge technologies such as adaptive optics    in which the lens or mirror is constructed from lots of carefully aligned tiny lenses and mirrors that can be manipulated using computers. A range of rapidly changing distortions can be minimized by deforming or tilting the tiny lenses and mirrors. The use of adaptive optics in vision correction is a current area of research.

An aerial overview of the central region of the Square Kilometre Array with the five kilometer diameter cores of antennas or dishes is seen. S K A-low array and S K A-mid array, which are phased arrays of simple dipole antennas to cover the frequency range from seventy to two hundred megahertz and two hundred to five hundred megahertz in circular stations, are also displayed.
An artist’s impression of the Australian Square Kilometre Array Pathfinder in Western Australia is displayed. (credit: SPDO, XILOSTUDIOS)

Test prep for ap courses

Which of the following is an advantage to using a concave mirror in the construction of a telescope?

  1. The telescope can gather more light than a telescope using lenses.
  2. The telescope does not suffer from chromatic aberration.
  3. The telescope can provide greater magnification than a telescope using lenses.
  1. I and III only
  2. II only
  3. I and II only
  4. I, II, and III


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A spherical mirror is used to construct a telescope.

  1. Using the picture below, draw two rays incident on the object mirror and continue their path through the eye lens.
    The image shows three shapes. At the lower left, there is an ellipse with horizontal axis. Above the ellipse is a small, tilted plane. On the right side is a vertical, curved shape (one side concave and one convex).
  2. The plane mirror is replaced with a concave lens. Using the picture below, draw the path of two incident rays.
    The image shows two shapes. On the left is a vertical shape with concave sides. On the right is a vertical, curved shape (one side concave and one convex).
  3. Using the concave lens setup, describe the final image created by the concave lens.
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Two concave lenses, of focal lengths 500 mm and 20 mm, are used in the construction of a telescope. Given any potential arrangement, what is the largest possible magnification the telescope may have?

  1. 100×
  2. 10,000×
  3. 25×


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Section summary

  • Simple telescopes can be made with two lenses. They are used for viewing objects at large distances and utilize the entire range of the electromagnetic spectrum.
  • The angular magnification M for a telescope is given by
    M = θ θ = f o f e ,
    where θ is the angle subtended by an object viewed by the unaided eye, θ is the angle subtended by a magnified image, and f o size 12{f rSub { size 8{o} } } {} and f e size 12{f rSub { size 8{e} } } {} are the focal lengths of the objective and the eyepiece.

Conceptual questions

If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?

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Problem exercises

Unless otherwise stated, the lens-to-retina distance is 2.00 cm.

What is the angular magnification of a telescope that has a 100 cm focal length objective and a 2.50 cm focal length eyepiece?

40 . 0 size 12{ - {underline {"40" "." 0}} } {}

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Find the distance between the objective and eyepiece lenses in the telescope in the above problem needed to produce a final image very far from the observer, where vision is most relaxed. Note that a telescope is normally used to view very distant objects.

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A large reflecting telescope has an objective mirror with a 10 . 0 m size 12{"10" "." 0`m} {} radius of curvature. What angular magnification does it produce when a 3 . 00 m size 12{3 "." "00"`m} {} focal length eyepiece is used?

1 . 67 size 12{ - 1 "." "67"} {}

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A small telescope has a concave mirror with a 2.00 m radius of curvature for its objective. Its eyepiece is a 4.00 cm focal length lens. (a) What is the telescope’s angular magnification? (b) What angle is subtended by a 25,000 km diameter sunspot? (c) What is the angle of its telescopic image?

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A 7.5× size 12{7 "." 5 times } {} binocular produces an angular magnification of 7 . 50 size 12{ - 7 "." "50"} {} , acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a 75.0 cm focal length, what is the focal length of the eyepiece lenses?

+ 10.0 cm size 12{+"10" "." 0`"cm"} {}

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Construct Your Own Problem

Consider a telescope of the type used by Galileo, having a convex objective and a concave eyepiece as illustrated in [link] (a). Construct a problem in which you calculate the location and size of the image produced. Among the things to be considered are the focal lengths of the lenses and their relative placements as well as the size and location of the object. Verify that the angular magnification is greater than one. That is, the angle subtended at the eye by the image is greater than the angle subtended by the object.

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Questions & Answers

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what happens to the size of charge if the dielectric is changed?
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omega= omega not +alpha t derivation
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u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
do to be peaceful with any body
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the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
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define variable velocity
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displacement in easy way.
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binding energy per nucleon
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Because HE needs someone to dominate the earth (Gen. 1:26)
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ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
when we face electric shock these elements work as a conductor that's why we got this shock
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Practice Key Terms 2

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