Question

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

Answer 1

Hello

The light-collecting area of a telescope goes as the square of its aperture. Calling
`A_1=110~m` the aperture of the first telescope and
`A_2=10~m` the aperture of the Keck telescope, the ratio between the light collected by the former and the latter is

`r= (A_1^2)/(A_2^2)= ((110~m)^2)/((10~m)^2)=121`

Answer 2

Answer: 121 times greater

Step-by-step 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.