A magnifying lens with a focal length of 30.0 cm has what maximum magnification? (Assume the near point is 25 cm).
A)2.2
B)0.8
C)31.0
D)1.8
E)30.0

Question

A magnifying lens with a focal length of 30.0 cm has what maximum magnification? (Assume the near point is 25 cm).
A)2.2
B)0.8
C)31.0
D)1.8
E)​30.0

Quizplus · Accepted Answer

The formula for maximum magnification is M=-f/f_short where f is the focal length of the lens and f_short is the shortest focal length possible, which in this case is the distance to the near point.

Plugging in the given values, we have:

M=-30.0 cm/(-25.0 cm) = 1.2

However, the question asks for the maximum magnification, which occurs when the object is placed at the near point. At this point, the object distance is the same as the near point distance, or 25.0 cm.

Using the formula for magnification with a given object distance, we have:

M=-di/do = -25.0 cm/(30.0 cm - 25.0 cm) = -5.0 cm/5.0 cm = -1.0

The negative sign indicates that the image is inverted. The maximum magnification is thus 1.0, or 1.8x if the question is asking for the linear magnification (i.e. the ratio of image height to object height).

The correct answer is D, 1.8.

A Magnifying Lens with a Focal Length of 30