A concave spherical mirror has a radius of curvatureof 18.0 cm. Locate the image

Question

A concave spherical mirror has a radius of curvatureof 18.0 cm. Locate the imagefor each of the following object distances. (Enter 0for M and the distance if no image is formed.) (a) do = 36.0 cm
M = , cm ---Orientation---in front of the mirror, real, anduprightin front of the mirror, real, andinvertedbehind the mirror, virtual, and uprightbehind the mirror, virtual, and invertedno image is formed

(b) do = 18.0 cm
M = , cm ---Orientation---in front of the mirror, real, anduprightin front of the mirror, real, andinvertedbehind the mirror, virtual, and uprightbehind the mirror, virtual, and invertedno image is formed

(c) do = 9.0 cm
M = , cm ---Orientation---in front of the mirror, real, anduprightin front of the mirror, real, andinvertedbehind the mirror, virtual, and uprightbehind the mirror, virtual, and invertedno image is formed (a) do = 36.0 cm
M = , cm ---Orientation---in front of the mirror, real, anduprightin front of the mirror, real, andinvertedbehind the mirror, virtual, and uprightbehind the mirror, virtual, and invertedno image is formed

(b) do = 18.0 cm
M = , cm ---Orientation---in front of the mirror, real, anduprightin front of the mirror, real, andinvertedbehind the mirror, virtual, and uprightbehind the mirror, virtual, and invertedno image is formed

(c) do = 9.0 cm
M = , cm ---Orientation---in front of the mirror, real, anduprightin front of the mirror, real, andinvertedbehind the mirror, virtual, and uprightbehind the mirror, virtual, and invertedno image is formed

Explanation / Answer

given that radius of curvature = R = 18.0cm focal length = f = R/2 = 18.0cm/2 = 9.0cm when d0= 36.0cm from the mirror eq 1/d0 + 1/di = 1/f 1/di = 1/f - 1/d0          = 1/9 -1/36    di = 12.0cm    M = -di/d0 = -12/36 =-0.33 simillarly d0 = 18.0cm    1/di = 1/f - 1/d0 plug in values di = ----cm M = -di/do = ----- when d0 = 9.0cm 1/di = 1/f - 1/d0     pluf in values di =-----cm    M = -di/do = --------     pluf in values di =-----cm    M = -di/do = --------

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