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Suppose astronomers built a 110-meter telescope. how much greater would its light-collecting area be than that of the 10-meter keck telescope?

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skyluke89
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The light-collecting area of a telescope goes as the square of its aperture. Calling [tex]A_1=110~m[/tex] the aperture of the first telescope and [tex]A_2=10~m[/tex] the aperture of the Keck telescope, the ratio between the light collected by the former and the latter is
[tex]r= \frac{A_1^2}{A_2^2}= \frac{(110~m)^2}{(10~m)^2}=121 [/tex]

Answer: 121 times greater

Explanation:

The light collecting area is directly proportional to square of aperture:

A ∝ l²

Aperture of Keck Telescope = l₁ = 10 m

Aperture of 11 m telescope, l₂ = 110 m

Light collecting area of Keck telescope = A₁

Light collecting area of 110 m telescope = A₂

A₁ ∝ l₁²

A₂ ∝ I₂²

A₂/A₁ = I₂²/ l₁² = (110 m)²/(10 m)² = 121/1

Thus, the light collecting area of 110 m telescope is 121 times greater than 10 m telescope.

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