Optics
Compound microscope (angular)
A short-focus objective and eyepiece multiply to a large angular magnification for tiny nearby objects.
Compound microscope (angular) — interactive Optics simulation. A short-focus objective and eyepiece multiply to a large angular magnification for tiny nearby objects.
Compound microscope optics
A short-focus objective and eyepiece multiply to a large angular magnification for tiny nearby objects.
The objective creates a magnified real image just inside the eyepiece focal point; the eyepiece then acts as a magnifier on that image. Total angular magnification is approximately the product of objective transverse magnification and eyepiece magnifying power—typically hundreds of times for biological work.
- M = M_obj × M_eye
- Two-lens system
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- 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.
Variable roles
What you set:
- Tube length L (cm)
What you measure:
- System magnification M
How the investigation runs
- 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.
- Enable the system-magnification readout (the two-lens image chain's overall M).
- Set the tube length (objective-to-eyepiece separation) for each trial and record the resulting system magnification.
Governing equation
Compound Microscope System Magnification — M = m₁·m₂·…
A compound microscope's overall magnification is the product of the objective's and eyepiece's own image magnifications, M = m_o × m_e — each found from the thin-lens equation using the real two-lens image chain, not an idealized angular-magnification formula.
What the printable worksheet asks students to work out
- 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.
- 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.
Where this shows up beyond the lab
- 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.
- 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.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Microscope
- Select the objective lens
- Press Play
- Two-stage magnification
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.