Consider the total amount of light collected by a 4-m telescope observing a star for 10 minutes. if you wanted to collect the same amount of light with a 2-m telescope, how long would you have to observe?

5 minutes

Explanation:

Let X, be the time to observe light for the 2-m

Therefore,

If it takes 4-m telescope 10 minutes

then ⇒  X × 4-m = 2-m × 10

X minutes = 20/4 = 5 minutes

time 5 minutes

A short focal length will give a wide field of view but the objects in the field of view will appear small. A longer focal length will produce a larger image and a shorter focal length will produce a smaller image. The eyepiece is then used, much like a microscope, to magnify that image.

It will take 4-m telescope more time to view because of it's larger image

Magnification

The magnification of an astronomical telescope changes with the eyepiece used. It is calculated by dividing the focal length of the telescope (usually marked on the optical tube) by the focal length of the eyepiece (both in millimeters). Thus:

TELESCOPE FOCAL LENGTH / OCULAR FOCAL LENGTH = MAGNIFICATION

For example, a telescope with a 1000mm focal length using a 10mm ocular is operating at 100x magnification (1000/10=100).

reserve is the answer