A concave spherical mirror has radius of curvature of 19.2 cm. Choose the answer

Question

A concave spherical mirror has radius of curvature of 19.2 cm. Choose the answer below that best describes the image that is formed by an object that is located 9.0 cm in front of the mirror.

a) real, inverted, magnified 5x and is 18 cm in front of the mirror.
b) Virtual, upright, magnified 13x and is 88.7 cm behind mirror.
c) Virtual, upright, magnified 16x and is 144 cm behind mirror.
d)real inverted, magnified .78x and is 24.2 cm in from of the mirror.

Can you please show all work and solve the problem and not just list steps. I need to see how everything is set up and solved. Thanks

Explanation / Answer

focal length = f = R/2 = 19.2/2 = 9.6 cm we have, 1/v + 1/u = 1/f ( mirror formula) 1/v + 1/(-9) = 1/(-9.6) image distance = v =+144 cm As v is positive , it is formed behind mirror, and is a virtual image. Magnification = -v/u = -(144/-9) = 16 ( magnification is positive, henc eimage is upright) OPtion - c is correct !!

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