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Astronomy & space · lesson 4 of 4

Telescopes, resolution and observing data

A telescope collects light over an aperture. In a simple unobstructed comparison, collected power scales with diameter squared.

Grades 9–128 practice questionsNotes + worked examples
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Learn the ideas

Prerequisites: Areas, ratios and measurement uncertainty.

Aperture

A telescope collects light over an aperture. In a simple unobstructed comparison, collected power scales with diameter squared.

Resolution

Angular resolution differs from magnification. Diffraction gives a characteristic angle proportional to wavelength divided by aperture diameter.

Noise

Longer exposures can improve signal-to-noise in appropriate regimes, but detector noise, backgrounds, saturation and moving targets complicate the tradeoff.

Calibration

Dark frames, flats and reference observations address different measurement effects. A processed image should preserve records of its transformations.

Worked examples

Example 1

Two unobstructed circular telescopes have diameters D and 2D. Find the collecting-area ratio of the larger to the smaller.

Area scales with diameter squared.

4

Example 2

What is angular resolution?

Resolution concerns distinguishable angular separation.

Ability to distinguish close directions

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

1 Two unobstructed circular telescopes have diameters D and 2D. Find the collecting-area ratio of the larger to the smaller.

Show answer and explanation

4

Area scales with diameter squared.

2 What is angular resolution?

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Ability to distinguish close directions

Resolution concerns distinguishable angular separation.

3 At fixed aperture, shorter wavelength gives what diffraction-limited angular scale?

Show answer and explanation

A smaller angle

The characteristic diffraction angle scales as λ/D.

4 For a simplified photon-limited model SNR=sqrt(N), find SNR for N=400 detected signal photons with negligible background.

Show answer and explanation

20

sqrt(400)=20 under the stated assumptions.

5 Can enlarging a blurry image always reveal genuine new resolved detail?

Show answer and explanation

No

Magnification does not reverse lost resolution by itself.

6 Why should an observing report record exposure and calibration choices?

Sample answer and marking guidance

They affect noise, background, saturation and interpretation. Reproducible processing requires this context.

Credit measurement effects and reproducibility.

7 Give one reason a space telescope and a ground telescope can offer complementary evidence.

Sample answer and marking guidance

Atmospheric transmission and turbulence affect ground observations, while instrument wavelength coverage and operating constraints differ. Combining suitable measurements can reduce ambiguity.

Credit a relevant physical distinction without claiming all space telescopes outperform all ground telescopes.

8 If collected signal counts quadruple in the stated negligible-background photon model, by what factor does SNR change?

Show answer and explanation

2

SNR scales as square root of signal counts in that model.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.