The Compound Microscope: Two Lenses for High Magnification
1 · Predict
A compound microscope uses a short-focal-length objective lens close to the specimen, followed by an eyepiece. Does using two lenses in sequence achieve much higher magnification than either lens could alone?
- Yes — chaining two moderate magnifications multiplies them together, giving a much higher overall magnification than a single lens.
- No — using two lenses doesn't increase magnification beyond a single lens's limit.
- Magnification depends only on the eyepiece, not the objective.
2 · Set Up
- Open the compound-microscope preset and press Reset. The objective has f = 6 cm; the eyepiece has f = 8 cm, separated by 22 cm.
- Enable the objective's image-distance and system-magnification readouts.
- Set the specimen's distance from the objective for each trial and record the objective's image distance and the overall system magnification.
3 · Collect Data
| Specimen distance from objective (cm) | Objective's image distance (cm) | System magnification M |
|---|---|---|
| 10 | ||
| 12 | ||
| 14 |
Plot system magnification M (y-axis) against specimen distance (x-axis) for your three trials.
4 · Analyze
- For one trial, compute the objective's image distance d_i1 from 1/f₁ = 1/d_o1 + 1/d_i1 (f₁ = 6 cm), then the eyepiece's object distance d_o2 = 22 − d_i1, then its image distance d_i2 from 1/f₂ = 1/d_o2 + 1/d_i2 (f₂ = 8 cm). Finally M = (−d_i1/d_o1)·(−d_i2/d_o2). Compare M to the table.
- This preset's default specimen distance (12 cm) gives M = 4. Explain, using the chain calculation, how a modest objective magnification combined with a modest eyepiece magnification compounds into a much larger overall number.
5 · Extend
- A specimen placed just barely outside the objective's focal length (as in this experiment) produces a large first-stage magnification. Explain why microscope objectives are designed with very short focal lengths (a few mm in real instruments) to maximize this effect.
- Compound microscopes can't magnify indefinitely — beyond a certain point, magnifying further just enlarges blur without revealing new detail, limited by the wavelength of light itself (diffraction). Why might simply adding more lens stages not solve this fundamental limit?
The Physics Behind This Experiment
Two-Stage Microscope Magnification
A compound microscope's overall magnification is the product of the objective's magnification (imaging the specimen) and the eyepiece's magnification (re-imaging that intermediate image): M = m_objective × m_eyepiece.