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
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
- Angular magnification
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 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?
Predictions to weigh
- 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.
Variable roles
What you set:
- Specimen distance from objective (cm)
What you measure:
- Objective's image distance (cm)
- System magnification M
How the investigation runs
- 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.
Governing equation
Two-Stage Microscope Magnification — M = m₁·m₂·…
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.
What the printable worksheet asks students to work out
- 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.
Where this shows up beyond the lab
- 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?
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Compound Microscope
- Select the object
- Press Play
- Objective plus eyepiece
- 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.