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Telescopes

Waves, sound and light · level 7, lesson 4 of 6

A question to start

Galileo's first telescopes, around 1610, were made of two small lenses in a tube. How do two lenses make faraway things look closer?

The idea

A simple refracting telescope has two converging lenses:

  1. The objective, with a long focal length \(f_o\), makes a real image of the distant object at its focal point.
  2. The eyepiece, with a short focal length \(f_e\), acts as a magnifying glass on that image.

With the two focal points together, the lenses are \(f_o + f_e\) apart, and the angular magnification is

\[M = \frac{f_o}{f_e}.\]

The telescope makes things look \(M\) times bigger in angle.

The size of the objective, the aperture, matters too. A wider lens or mirror catches more light, so faint things show up, and it can separate finer detail. Big modern telescopes use curved mirrors instead of lenses, because large mirrors are easier to make and support.

objective, f_oeyepiece, f_eshared focus

Worked examples

1. Magnification. \(f_o = 1.0\) m, \(f_e = 0.025\) m: \(M = 1.0/0.025 = 40\).

2. Length. The tube is about \(1.0 + 0.025 = 1.025\) m long.

3. Changing eyepieces. Swap to \(f_e = 0.010\) m: \(M = 100\). But the image is dimmer and blurrier, because the same light is spread over a bigger view.

Try it

  1. Which lens of a telescope has the longer focal length?
  2. Find \(M\) for \(f_o = 0.90\) m and \(f_e = 0.018\) m.
  3. Why does a telescope with a bigger aperture show fainter stars?
  4. Why do the largest telescopes use mirrors rather than lenses?
Answers
  1. The objective.
  2. \(0.90/0.018 = 50\).
  3. It collects more light.
  4. Large mirrors are easier to make and to support than large lenses.

Common mistake

"More magnification always shows more." Beyond a point, extra magnification only makes a blurry image bigger. The aperture limits how much detail there is to see.

Where it leads