Question 33.14: A jeweler's "loupe." An 8-cm-focal-length converging lens is......
A jeweler’s “loupe.” An 8-cm-focal-length converging lens is used as a “jeweler’s loupe,” which is a magnifying glass. Estimate (a) the magnification when the eye is relaxed, and (b) the magnification if the eye is focused at its near point N=25 \mathrm{~cm}.
APPROACH The magnification when the eye is relaxed is given by Eq. 33-6a. When the eye is focused at its near point, we use Eq.33-6b and we assume the lens is near the eye.
M=\frac{\theta^{\prime}}{\theta}=\frac{h / f}{h / N}=\frac{N}{f} \cdot\left[\begin{array}{c}\text { eye focused at } \infty ; \\N=25 \mathrm{~cm} \text { for normal eye }\end{array}\right] (33-6a)
M=\frac{N}{f}+1 . \quad\left[\begin{array}{c}\text { eye focused at near point, } N ; \\N=25 \mathrm{~cm} \text { for normal eye }\end{array}\right] (33-6b)
(a) With the relaxed eye focused at infinity,
M=\frac{N}{f}=\frac{25 \mathrm{~cm}}{8 \mathrm{~cm}} \approx 3 \times
(b) The magnification when the eye is focused at its near point (N=25 \mathrm{~cm}), and the lens is near the eye, is
M=1+\frac{N}{f}=1+\frac{25}{8} \approx 4 \times