How far from a lens having a focal length of +50 mm must the object be placed if it is to form a virtual image that is 3.0 times the size of the object?
A)33 mm
B)42 mm
C)48 mm
D)54 mm

Question

Quizplus · Accepted Answer

For a lens (convex in this case, given the positive focal length), the magnification (m) is related to the object distance (u) and the image distance (v) by the formula m = -v/u. Given that the image is virtual and magnified 3 times the size of the object, m = -3. Also, using the lens formula 1/f = 1/v + 1/u, where f is the focal length (+50 mm), we can solve for u. Substituting m = -v/u into the lens formula gives us two equations with two unknowns. Solving these equations with the given values (and considering the sign convention for a virtual image where v is negative and u is positive), we find that the object must be placed 33 mm from the lens to achieve the described conditions.

How Far from a Lens Having a Focal Length of +50