Explain formation of image by concave mirror when the object is placed at infinity.

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mwmovr40 | College Teacher | (Level 1) Associate Educator

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According to the thins lens/mirror equation:

(1/F) = (1/Di) + (1/Do)  where F is the focus, Di is the distance from the mirror to the formation of the image, and Do is the distance from the mirror to the object.

If the object is the Sun (or "infinitely far away") then Do is extremely large.  1 divided by an extremely large number approaches zero and in fact for the Sun Do is about 150,000,000,000 meters makes 1/Do = 0 to a large number of significant digits.

Therefore, when Do is extremely large

(1/F) = (1/Di) + 0

(1/F) = (1/Di)

F = Di

Therefore, the image is located at the focus of the mirror.

The size of the image is determined by the magnification equation

M = -Di/Do  Again, because Do is extremely large Di/Do approaches zero which is telling us that the rays of the Sun are concentrated to a single point at the focus and therefore is much brighter than it would be if it weren't focused to that point.

One could also do a ray diagram.  Rays from infinately distant objects are considered to be parallel.  Parallel rays striking a concave mirror are reflected through a single point at the focus.  See the link below (scroll about 2/3 down web page)

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