A section of a sphere with a radius of curvature of 20 cm is mirrored on both th

Question

A section of a sphere with a radius of curvature of 20 cm is mirrored on both the inner (concave) and the outer (convex) surfaces. (a) A 2.0 cm high object is 30 cm from the concave surface of the mirror. Where is the image, how hight is it and what are its characteristics, i.e., is it real or virtual, upright or inverted, and enlarged or reduced? (b) Repeat the problem, only now with the object 30 cm in in front of the convex side of the mirror. (c) Provide a ray diagram for each situation.

Please show all work so I can follow with ease.

Explanation / Answer

concave mirror

1/S +1/S' = 2/R

1/30 + 1/S' = 2/20 = 1/10

S'= (30*10)/(30-10) = 300/20 = 15 cm

hi/h = -s'/s

hi = -(15*2)/30 = -1 cm

image is real , inverted and smaller

b) convex mirror

1/S + 1/S' = 2/R

1/30 + 1/S' = -2/20 = -1/10

S'= -(30*10)/(30+10) = 300/40 = -7.5 cm

hi/h = -s'/s

hi = (7.5*2)/30 = 0.5 cm

image is virtual , erected and smaller

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