You have just learned that NASA has two concave spherical mirrors, which they ar
ID: 1696344 • Letter: Y
Question
You have just learned that NASA has two concave spherical mirrors, which they are willing to give away to an educational organization. The larger mirror has a radius of 6.0 meters and the smaller a radius of 14/15 meters. You hope to talk McWane Center into requesting these mirrors and constructing an observatory, which would project an image of the Sun every noontime onto the floor of an exhibit. The large mirror already has a big circular hole cut out along its optical axis. You think the larger mirror could be mounted on the roof with the concave side, pointing straight upward. Then the smaller mirror could be placed inside the first with concave side facing downward. The goal is to project the final image of the sun through the hole in the larger mirror and through a skylight in the roof and finally onto the display floor. You know from visiting McWane Center this floor is exactly 4.0 meters below the point on the roof where the vertex of the larger mirror could be mounted. In order to convince the managers your idea is feasible, you have to determine exactly where to mount the smaller mirror in order to create a focused image of the sun on the floor below. It would help your case if you could estimate how large the image of the sun would be on the exhibit floor.Explanation / Answer
Given that lens of the small mirror radius r = 14/15 m
= 0.93m
focal length of the small mirror is f = r / 2
= 0.93m /2
= 0.46m
lens of the larger mirror radius R = 6.0m
focal length F = R / 2
= 3.0 m
object distance d_0 = 4.0 m
1/ f_1 - 1/ f_2 = 1/ d_0 +1/d_i
1/ 0.46 m - 1/ 3.0 m = 1/ 4.0 m +1/ d_i
d_i = 0.628 m
d_o = L - d_i
L = 4.628m
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