I need an answer to the following multi-part question, and I would appreciate a

Question

I need an answer to the following multi-part question, and I would appreciate a detailed explanation please. A lamp which is 7.5 cm tall is in front of a concave mirror which has a focal length of 91.5 cm. (a) How tall is the lamp's image if the lamp is a distance of 9.2 cm from the mirror (include sign if negative)? cm (b) How tall is the lamp's image if the lamp is a distance of 146.4 cm from the mirror (include sign if negative)? cm (c) How tall is the lamp's image if the lamp is a distance of 411.8 cm from the mirror (include sign if negative)? cm (d) When a concave mirror forms a real image, is the image always enlarged? yes no (e) In general, for a concave mirror with focal length, +f, how far should an object be placed from the mirror to form a real image which is neither enlarged nor reduced (enter your answer as a multiple of f)? (f) If you want the real image to be enlarged, should the object be closer to the mirror than the distance found in (e) or farther from the mirror?

Explanation / Answer

Given, ho = 7.5 cm f = 91.5 cm (f taken negative with sign convention) a) u = -9.2 cm ; f = -91.5 cm 1/u + 1/v = 1/f ; solving, we get, v = 10.23 cm (right side of mirror) m = -v/u = hi/ho ; hi = -v*ho/u = -10.23*7.5/(-9.2) = 8.33 cm (virtual image) b) u = - 146.4 cm using same fformula, v = -244 cm (left of mirror) m = -v/u = hi/ho ; hi = -12.5 cm (Real, inverted) c) u = -411.8 cm v = -117.64 cm (left of mirror) hi = -2.143 cm (inverted, small, real) d) No. (it can be small too) e) 2f f) closer to the mirror than 2f

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