Compound Microscope: Tube Length and Magnification

1 · Predict

A compound microscope's objective and eyepiece have fixed focal lengths, but the eyepiece's position — the tube length — can still be adjusted. Does changing the tube length change the microscope's overall (system) magnification, even though neither lens's focal length changes?

• No — tube length doesn't affect overall magnification, only the individual lens focal lengths do.
• Only the eyepiece's focal length matters, not how far it sits from the objective.
• Yes — increasing the tube length moves the eyepiece closer to its own focal point (relative to the real image the objective forms), which increases the eyepiece's own magnification and multiplies into a larger overall system magnification.

2 · Set Up

1. Open the microscope preset and press Reset. The objective (f_o = 8 cm, at a fixed specimen distance) forms a real image; the eyepiece has f_e = 25 cm.
2. Enable the system-magnification readout (the two-lens image chain's overall M).
3. Set the tube length (objective-to-eyepiece separation) for each trial and record the resulting system magnification.

3 · Collect Data

Plot system magnification M (y-axis) against tube length L (x-axis) for your three trials. Is the relationship a straight line?

4 · Analyze

1. For one trial, first find the objective's image distance d_i1 from 1/f_o = 1/d_o1 + 1/d_i1 (d_o1 = 9.6 cm, f_o = 8 cm — this stays the same at every tube length). Then find the eyepiece's object distance d_o2 = L − d_i1, and its image distance d_i2 from 1/f_e = 1/d_o2 + 1/d_i2 (f_e = 25 cm). Finally M = (−d_i1/d_o1)·(−d_i2/d_o2). Compare M to the table.
2. Explain why the objective's own magnification stays constant across all three trials, while the eyepiece's magnification — and so the overall system magnification — changes with tube length.

5 · Extend

1. Compare this experiment's system magnification to the simple-magnifier experiment's M = N/f. Explain why chaining two real lens images together can multiply magnification far beyond what either lens could produce alone.
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 the tube length — not just each lens's focal length — matters for interchangeable microscope parts.

The Physics Behind This Experiment

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