Parallel light from a distant object strikes the large mirror in the figure and

Question

Parallel light from a distant object strikes the large mirror in the figure and is reflected by the small mirror that is 2.528 m from the large mirror and is actually spherical in curvature not planar as shown. The large mirror has a radius of curvature of 7.90 m. The light reflected from the second mirror is focused at a small hole at the vertex of the first (larger) mirror. What is the distance from the large mirror to the image that it produces, which becomes the object for the second mirror? What is the radius of curvature of the smaller mirror?

Explanation / Answer

For the large mirror first, apply 1/f = 1/p + 1/q. Since the light is coming from a parallel source, the object distance is considered infinite. Also, we know that the focal length is half the radius of curvature

1/3.95 = 1/ + 1/q

q = 3.95 m

This the image produced from the large mirror is 3.95 m away from it.

Then, for the second mirror, apply 1/f = 1/p + 1/q

Since the two mirrors are 2.528 m apart, and the image from the first is the object from the second, we can find the object distance. 3.95 - 2.528 = 1.422 m. The image is formed on the first mirror and that is 2.528 m away, thus

1/f = 1/1.422 + 1/2.528

f = .91 m

R = 2f

R = 1.82 m

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