Answer
a. $9.0\times$.
b. $1.8\times$.
Work Step by Step
Calculate the focal length of the magnifying glass, using the magnification of 3.0 and equation 25–2a, which applies for a relaxed eye (i.e., one that is focused at infinity).
$$M=\frac{N}{f}$$
$$f=\frac{N}{M}=\frac{25.0cm}{3.0}=8.33cm$$
a. Now, apply equation 25–2a for a near point of N = 75 cm.
$$M=\frac{N}{f}=\frac{75cm}{8.33cm}=9.0\times$$
The closest that an object can be viewed by the unaided eye is the near point.
A “large” or “distant” near point of 75 cm means that without the lens, the object subtends a smaller angle than normal, so with the lens, the magnification is greater than 3.0.
b. Now, apply equation 25–2a for a near point of N = 15 cm.
$$M=\frac{N}{f}=\frac{15cm}{8.33cm}=1.8\times$$
The closest that an object can be viewed by the unaided eye is the near point.
A “small” near point of 15 cm means that without the lens, the object subtends a larger angle than normal, so with the lens, the magnification is smaller than 3.0.
