Question

An object is positioned 21 cm from a spherical concave mirror of unknown focal length. The image that is formed is 30 cm from the mirror. (a) Calculate the focal length. (Enter NONE if a particular answer does not exist.) postive image distance cm negative image distance cm (b) Is this answer unique? Yes, there is only one possible focal length. No, there are two possible focal lengths. (c) Is the image real or virtual? The image is real. The image is virtual. Both images are real. Both images are virtual. One image is real and the other is virtual. The image is neither real nor virtual. (d) If the object is 10 cm tall, determine the height of the image(s). postive image distance cm negative image distance cm

Answer 1

object distance s = 21 cm

image distance s' = 30 cm

(a)

If the image is real

image distance s' = 30 cm

from mirror equation

1/s + 1/s' = 1/f

1/21 + 1/30 = 1/f

f = 12.35 cm

If the image is virtual

image distance s' = -30 cm

1/21 - 1/30 = 1/f

f = 70 cm

(b)

No, there are two possible focal lengths.

(c)

One image is real and the other is virtual

(d)

magnification M = -s'/s = y'/y

image height y' = y*(-s'/s) = 10*(-30/21) = -14.3 cm

for negative image distance

image height y' = y*(-s'/s) = 10*(30/21) = 14.3 cm