Example 6.1: Calculating the Light-Collecting Area

What is the area of a 1-m diameter telescope? A 4-m diameter one?

Solution

Using the equation for the area of a circle,

$\displaystyle A=\frac{\pi d^{2}}{4}$

the area of a 1-m telescope is

$\displaystyle \frac{\pi d^{2}}{4} =\frac{\pi(1\,\text{m})^{2}}{4} =0.79\,\text{m}^{2}$

and the area of a 4-m telescope is

$\displaystyle \frac{\pi d^{2}}{4} =\frac{\pi(4\,\text{m})^{2}}{4} =12.6\,\text{m}^{2}.$

Check Your Learning

Show that the ratio of the two areas is 16:1.

Answer:

$\displaystyle \frac{12.6\,\text{m}^{2}}{0.79\,\text{m}^{2}}=16.$

Therefore, with 16 times the area, a 4-m telescope collects 16 times the Light of a 1-m telescope.

Attribution

Access for free at openstax.org.

Bibliography

This entry is a derivative work of the original March 9, 2022 release identified in [1].

[1] Andrew Fraknoi, David Morrison, and Sidney C. Wolff, Astronomy 2e. Houston, Texas: OpenStax, March 9, 2022. Digital ISBN 978-1-951693-50-3. Textbook content produced by OpenStax in this edition is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0), except where otherwise noted. Changes: converted to LaTeX for PhysicsLibrary. Access for free at openstax.org.

"calculating the light collecting area of a telescope" is owned by bloftin.
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