The Simple Magnifier: Angular Magnification

1 · Predict

A simple magnifying glass, used with a relaxed eye, has its object placed exactly at the lens's focal point. Does a shorter-focal-length lens give a higher or lower angular magnification?

• Higher — a shorter focal length lets you get much closer to the object than the eye's unaided near point would allow, producing a larger apparent angular size.
• A shorter focal length gives lower magnification.
• Magnification doesn't depend on the lens's focal length.

2 · Set Up

1. Open the simple-magnifier preset and press Reset. The object sits exactly at the lens's focal point (relaxed-eye viewing, virtual image at infinity).
2. Enable the angular-magnification readout.
3. Set the lens's focal length for each trial and record the resulting angular magnification.

3 · Collect Data

Plot M (y-axis) against 1/f (x-axis) for your three trials. Is the line straight through the origin?

4 · Analyze

1. For one trial, compute M = N/f using the standard near-point distance N = 25 cm. Compare to the table.
2. Explain why a shorter focal length gives higher magnification: it lets the relaxed eye view the object from much closer than its own unaided near point would ever allow, making the object subtend a much larger angle.

5 · Extend

1. Very short focal length magnifiers (giving high M) also have very short working distances (the object nearly touches the lens), which becomes impractical past a certain magnification. Explain why jeweler's loupes and simple hand magnifiers rarely exceed about 10×–20×.
2. For much higher magnification than a simple lens can practically achieve, optical designers switch to compound systems (like the compound-microscope experiment). Explain why chaining two moderate-magnification stages together, rather than using one extremely short-focal-length lens, is the practical solution.

The Physics Behind This Experiment

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