A lens with f= 10.0 cm is held 45.0 cm from an object. What is
the image distance?
(Unit = cm)
it is not 12 cm.

8.2 cm

Explanation:

1/f = 1/so + 1/si

1/10 = 1/45 + 1/si

1/si = 1/10 - 1/45

1/si = 9/90 - 2/90

1/si = 7/90

si = 90/7 = 12.86 cm.

since you said that the answer was not 12 them the lens must be concave with negative (minus) focal length

1/f = 1/so + 1/si

- 1/10 = 1/45 + 1/si

1/si = - 1/10 - 1/45

1/si = -9/90 - 2/90

1/si = -11/90

si = -90/11 = - 8.2 cm

- (read: minus or negative sign) indicates the image is in the same side of the object

hope its true and can help you

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