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 = −f₁/f₂
- 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 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?
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 the tube length.
- Yes — a longer tube length increases the objective's own image magnification, which multiplies into the overall system magnification.
Variable roles
What you set:
- Tube length L (cm)
What you measure:
- Angular magnification M
How the investigation runs
- Open the microscope preset and press Reset. The objective has f_o = 8 cm; the eyepiece has f_e = 25 cm.
- Enable the angular-magnification readout.
- Set the tube length (objective-to-eyepiece separation) for each trial and record the resulting magnification.
Governing equation
Compound Microscope Magnification — M = −(L/f_o)(N/f_e)
A compound microscope's total angular magnification is M = −(L/f_o)(N/f_e): the objective's magnification over the tube length L, multiplied by the eyepiece's simple-magnifier factor using the standard near point N = 25 cm.
What the printable worksheet asks students to work out
- 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.
- 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).
Where this shows up beyond the lab
- 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.
- 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.
- 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.