Optics
Two-lens enlarger
Two converging lenses in series project an enlarged real image — the overall magnification is the product of the stages.
Two-lens enlarger — interactive Optics simulation. Two converging lenses in series project an enlarged real image — the overall magnification is the product of the stages.
Two-lens enlarger
Two converging lenses in series project an enlarged real image — the overall magnification is the product of the stages.
Similar stacking of converging lenses, but arranged to project an enlarged real image onto a screen or film. Each stage contributes magnification multiplied across the train—used in photographic enlargers and some projection systems.
- Real enlarged image
- M = product of stages
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
Unlike a compound microscope's typically virtual final image, a photographic enlarger needs to project a REAL, enlarged image onto photo paper. Can two converging lenses in sequence still produce a real (not virtual) final image?
Predictions to weigh
- No — chaining two lenses always produces a virtual final image.
- It depends only on the object distance, not the lens arrangement.
- Yes — with the right spacing and focal lengths, the two-lens chain's final image lands as real, ready to project onto a surface.
Variable roles
What you set:
- Object distance from L1 (cm)
What you measure:
- L1's image distance (cm)
- System magnification M
How the investigation runs
- Open the compound-enlarger preset and press Reset. L1 has f = 8 cm; L2 has f = 12 cm, separated by 34 cm.
- Enable L1's image-distance and system-magnification readouts.
- Set the object distance from L1 for each trial and record L1's image distance and the overall system magnification.
Governing equation
Two-Stage Enlarger Magnification — M = m₁·m₂·…
Like any compound lens chain, the enlarger's system magnification is the product of its two lenses' individual magnifications: M = m₁ × m₂. Careful choice of focal lengths and spacing ensures the final image lands real (not virtual), ready to project.
What the printable worksheet asks students to work out
- For one trial, compute L1's image distance d_i1 from 1/f₁ = 1/d_o1 + 1/d_i1 (f₁ = 8 cm), then L2's object distance d_o2 = 34 − d_i1, then its image distance d_i2 from 1/f₂ = 1/d_o2 + 1/d_i2 (f₂ = 12 cm). Finally M = (−d_i1/d_o1)·(−d_i2/d_o2). Compare M to the table.
- This preset's default object distance (16 cm, L1's 2f point) gives M = 2 with a REAL final image. Explain why checking d_i2's sign (positive = real) matters for whether this system could actually project onto photo paper.
Where this shows up beyond the lab
- For an enlarger to work, its final image must land at a positive (real) distance beyond L2, at the exact height where the photo paper sits. Explain why an enlarger's design must carefully control both lenses' focal lengths and spacing to guarantee this.
- Compare this experiment's default M = 2 (real final image) to compound-relay's M = 1 and compound-microscope's M = 4 (typically viewed as virtual through an eyepiece). Explain why the SAME two-lens chain math (product of magnifications) can produce such different practical outcomes depending on the specific focal lengths and spacing chosen.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Compound Enlarger
- Select the object
- Press Play
- Enlarged intermediate image
- 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.