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A certain telescope has an objective mirror with an aperture diameter of $200 . \mathrm{mm}$ and a focal length of $2.00 \times 10^{3} \mathrm{mm} .$ It captures the image of a nebula on photographic film at its prime focus with an exposure time of 1.50 $\mathrm{min} .$ To produce the same light energy per unit area on the film, what is the required exposure time to photograph the same nebula with a smaller telescope that has an objective with a 60.0 -mm diameter and a 900 -mm focal length?
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{'transcript': "here we have Ted or not equals negative. A prime over. If not so we find that age prime equals negative data, not times two major Now we want equals I not a one equals I know times by our square all he's 0.1 major square of that we have you wan equals B Juan de 30 one. It was, I know by you don't want one meter square times 1.5 I mean it. No. Similarly, we can find Ito equals P to tell 32. It was, I know lives by See the point 03 meter square time still dirty. Do no taking a rescue off that because we have same amount of light energy cummings per unit area. Using that, we can find your 30 do equals. Seen a point, do over 0.6 squares tires. 0.9 over to square times 1.5 minute. It was 3.38 Meaning"}