Compound Microscope Magnification: The Full Formula

1 · Predict

A compound microscope's total angular magnification depends on the tube length (distance between objective and eyepiece), not just their individual focal lengths. Does a longer tube length increase the overall magnification?

• No — tube length doesn't affect overall magnification, only the individual lens focal lengths do.
• Only the eyepiece's focal length matters, not the tube length.
• Yes — a longer tube length increases the objective's own image magnification, which multiplies into the overall system magnification.

2 · Set Up

1. Open the microscope preset and press Reset. The objective has f_o = 8 cm; the eyepiece has f_e = 25 cm.
2. Enable the angular-magnification readout.
3. Set the tube length (objective-to-eyepiece separation) for each trial and record the resulting magnification.

3 · Collect Data

Plot M (y-axis) against tube length L (x-axis) for your three trials. Is the line straight through the origin?

4 · Analyze

1. For one trial, compute M = −(L/f_o)·(N/f_e) using f_o = 8 cm, f_e = 25 cm, N = 25 cm (standard near point). Compare to the table.
2. Explain why this formula combines both a 'lateral' magnification factor (L/f_o, from the objective's imaging over the tube length) and an 'angular' magnification factor (N/f_e, from the eyepiece acting as a simple magnifier on that intermediate image).

5 · Extend

1. Compare this experiment's formula to the simple-magnifier experiment's M = N/f. Explain why the microscope's extra factor L/f_o represents the 'pre-magnification' step the objective lens contributes before the eyepiece even gets involved.
2. Real microscopes historically standardized on specific tube lengths (like 160 mm) so objectives and eyepieces from different manufacturers could be mixed and matched predictably. Explain why standardizing L (alongside f_o and f_e) matters for interchangeable microscope parts.

The Physics Behind This Experiment

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