Question

Shown following are the primary mirror arrangements and total light-collecting area of five different telescopes. Notice that although the arrangements look similar to those in Part B, the light-collecting areas are not the same. Also listed is an amount of time (exposure time) that each telescope will be pointed at the same distant galaxy. Again assume that the quality of these mirrors, the detectors, and the observing conditions are identical. Rank the telescopes from left to right based on the brightness of the image each telescope will take of the galaxy in the time indicated, from brightest to dimmest. To rank two (or more) telescopes as equal, drag one on top of the other(s).

Answer 1

Exposure duration is inversely proportional to the area of the lens, emulation emulsion speed and subject brightness. If we called the exposure duration “t” for time in seconds, the lens area “A”, the emulsion or sensor speed “S”, and the subject brightness “B” we have:

A x S x B = 1/t

(since sensor speed is not mentioned consider it a constant)

B = 1/(t x A x S)

1. B = 1/(10 x 120 x S) = 1/1200S
2. B = 1/(2 x 600 x S) = 1/200S
3. B = 1/(5 x 240 x S) = 1/200S
4. B = 1/(1 x 1200 x S) = 1/200S
5. B = 1/(20 x 60 x S) = 1/200S

All of the telescopes are equal, so all of them go in the middle.

Brightest
(all answer options)
Dimmest