A magnifying lens of power d (in diopters)gives what magnification when the viewing eye is relaxed assuming a near point of 25 cm?
A)25d
B)0.25/d
C)d/4
D)The correct answer is not given.

Question

Quizplus · Accepted Answer

The magnification given by a magnifying lens is M = 1/(1 - d/f), where f is the focal length of the lens. For a magnifying lens of power d (in diopters), the focal length is f = 1/d (in meters). Therefore, M = 1/(1 - d/(1/d)) = 1/(1 - d^2) = (1 + d)/(1 - d). When the viewing eye is relaxed, the near point is at 25 cm = 0.25 m, so the object distance for the lens is u = 0.25 m. The magnification is therefore M = (1 + d)/(1 - d) = [(1/d) + 1]/[(1/d) - 1]. Substituting d/4 for (1/d) gives M = (d/4 + 1)/(d/4 - 1), which simplifies to M = d/4. Therefore, the magnification given by a magnifying lens of power d (in diopters) when the viewing eye is relaxed is d/4.

A Magnifying Lens of Power D (In Diopters)gives What Magnification