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How does the light-collecting area of an 8-meter telescope compare to that of a 2-meter telescope? How does the light-collecting area of an 8-meter telescope compare to that of a 2-meter telescope? The 8-meter telescope has 8 times the light-collecting area of the 2-meter telescope. The 8-meter telescope has 16 times the light-collecting area of the 2-meter telescope. The 8-meter telescope has 4 times the light-collecting area of the 2-meter telescope. The answer cannot be determined from the information given in the question.

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Answer:

The 8-meter telescope has 16 times the light-collecting area of the 2-meter telescope.

Explanation:

Area of 8 meter telescope

[tex]A_1=\pi \frac{D^2}{4}\\\Rightarrow A_1=16\pi[/tex]

Area of 2 meter telescope

[tex]A_2=\pi \frac{D^2}{4}\\\Rightarrow A_1=1\pi[/tex]

Dividing the equations we get

[tex]\frac{A_1}{A_2}=\frac{16\pi}{1\pi}\\\Rightarrow A_1=16A_2[/tex]

Hence, the 8-meter telescope has 16 times the light-collecting area of the 2-meter telescope.  

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