A magnifying glass uses a converging lens with a refractive power of 20 diopters.What is the magnification if the image is to be viewed by a relaxed eye (image at the far point)having a near point of 25 cm and a far point at infinity?
A) 5.0 x
B) 3.0 x
C) 4.0 x
D) 1.0 x
E) 2.0 x

Question

Quizplus · Accepted Answer

The magnification (M) of a magnifying glass when the image is at the far point of a relaxed eye (considered at infinity) can be calculated using the formula M = 1 + (D/f), where D is the distance of the near point (in meters) and f is the focal length of the lens (also in meters). Given the refractive power of the lens is 20 diopters, the focal length (f) is the reciprocal of the refractive power, f = 1/20 meters = 0.05 meters. The near point is given as 25 cm, which is 0.25 meters. Plugging these values into the formula gives M = 1 + (0.25/0.05) = 1 + 5 = 6. However, considering the standard formula for magnification using a magnifying glass for a relaxed eye (image at infinity) is M = 25/f (in cm), where f is in cm. Given f = 5 cm (from 20 diopters = 1/0.05 m), M = 25/5 = 5. Thus, the correct magnification is 5.0x, indicating a mistake in my initial explanation regarding the formula application. The correct formula directly relates to the diopter value and the standard viewing distance (25 cm or 0.25 m), leading to the correct answer without the need for the additional step I initially described.

A Magnifying Glass Uses a Converging Lens with a Refractive