Question

how does the light-collecting area of an 8-meter telescope compare to that of a 4-meter telescope? the answer cannot be determined from the information given in the question. the 8-meter telescope has 64 times the light-collecting area of the 4-meter telescope. the 8-meter telescope has 16 times the light-collecting area of the 4-meter telescope. the 8-meter telescope has 4 times the light-collecting area of the 4-meter telescope.

Answer 1

When comparing an 8-meter telescope's light-collecting area to that of a 4-meter telescope, it is discovered that the 8-meter telescope has 4 times larger light-collecting area. The fourth statement is the correct one.

The telescope's light-collecting area is proportional to the space around its mirror-mounted objective lens. Then, the formula for this is written as A = R² = D²/4 where D is the lens or mirror diameter.

The area of the objective affects the ability to gather light. The square of the telescope's diameter determines the area. The diameter of a 4-meter telescope is 4 meters, whereas that of an 8-meter telescope is 8 meters. Then,

$\begin{aligned}\frac{A_8}{A_4}&=\frac{8^2}{4^2}\\&=\frac{64}{16}\\&=4\\A_8&=4\times A_4\end{aligned}$

Therefore, from this, we can tell the light-collecting area of the 8-meter telescope is 4 times greater than that of the light-collecting area of the 4-meter telescope.

To know more about the light-collecting area:

https://brainly.com/question/13450299

#SPJ4