AcademyGeometric Optics
Academy
Magnifiers
Level 1 - Physics topic page in Geometric Optics.
Principle
A magnifier increases angular size by letting the eye view a close virtual image comfortably.
Notation
\(M\)
angular magnification
1
\(f\)
magnifier focal length
\(\mathrm{m}\)
\(N\)
near point distance
\(\mathrm{m}\)
\(\theta\)
viewing angle with magnifier
\(\mathrm{rad}\)
\(\theta_0\)
unaided viewing angle at near point
\(\mathrm{rad}\)
Method
Derivation 1: Angular magnification
Angular magnification compares apparent angle with the unaided near-point angle.
Definition
\[M=\frac{\theta}{\theta_0}\]
Relaxed eye
\[M\approx\frac{N}{f}\]
Near-point image
\[M\approx1+\frac{N}{f}\]
The relaxed-eye form places the virtual image at infinity. The near-point form places the virtual image at the eye's near point.
Rules
Angular magnification
\[M=\theta/\theta_0\]
Relaxed magnifier
\[M=N/f\]
Near-point magnifier
\[M=1+N/f\]
Near point
\[N=25\,\mathrm{cm}\]
Examples
Question
Find relaxed-eye magnification for
\[f=5.0\,\mathrm{cm}\]
Answer
\[M=\frac{N}{f}=\frac{25\,\mathrm{cm}}{5.0\,\mathrm{cm}}=5.0\]
Checks
- A simple magnifier is a converging lens.
- Shorter focal length gives larger angular magnification.
- The image viewed through a magnifier is virtual.