A spherical silver Christmas tree ornament, 17 cm in diameter, acts as a mirror.

Question

A spherical silver Christmas tree ornament, 17 cm in diameter, acts as a mirror. (a) Are the images one sees in it real or virtual, upright or inverted? (Select all that apply.)
real virtual upright inverted

(b) Find the image height of a man 1.9 m tall, standing 4.0 m from the ornament.

A spherical silver Christmas tree ornament, 17 cm in diameter, acts as a mirror. (a) Are the images one sees in it real or virtual, upright or inverted? (Select all that apply.)
real virtual upright inverted

(b) Find the image height of a man 1.9 m tall, standing 4.0 m from the ornament.
(a) Are the images one sees in it real or virtual, upright or inverted? (Select all that apply.)
real virtual upright inverted

(b) Find the image height of a man 1.9 m tall, standing 4.0 m from the ornament.
real virtual upright inverted real virtual upright inverted

Explanation / Answer

      diameter of spherical christmas tree d = 17 cm          radius   r = 8.5 cm        focal length of the mirror   f = R /2   = 4.25 cm     object distance   d_o    = 4 m = 400 cm      image distance    d _ i = ?                      equation of spherical mirror is                1 / d_o + 1 / d_ i   = 1 /f                          =  1 / 4.25 - 1 / 400                         d_ i = 4.29 cm     image is real image               Magnification                   M = - d_i / d_ o                      = 4.29 / 4.25                      = -1 image is inverted

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