A Two-Lens Relay: Chaining Images Together
1 · Predict
Two identical converging lenses are placed so the first lens's image becomes the second lens's object. Does the overall system magnification simply multiply the two lenses' individual magnifications?
- Yes — system magnification is the product of each lens's individual magnification: M = m₁ × m₂.
- System magnification is the sum of the individual magnifications.
- System magnification can't be predicted from the individual lens magnifications.
2 · Set Up
- Open the compound-relay preset and press Reset. Both lenses have f = 10 cm, separated by 40 cm.
- Enable the first-lens image-distance and system-magnification readouts.
- Set the object distance from lens 1 for each trial and record the first image distance and overall system magnification.
3 · Collect Data
| Object distance from L1 (cm) | L1's image distance (cm) | System magnification M |
|---|---|---|
| 14 | ||
| 20 | ||
| 26 |
Plot system magnification M (y-axis) against L1's object distance (x-axis) for your three trials.
4 · Analyze
- For one trial, compute L1's image distance d_i1 from 1/f₁ = 1/d_o1 + 1/d_i1 (f₁ = 10 cm), then L2's object distance d_o2 = 40 − d_i1, then L2's image distance d_i2 from 1/f₂ = 1/d_o2 + 1/d_i2 (f₂ = 10 cm). Finally M = (−d_i1/d_o1)·(−d_i2/d_o2). Compare M to the table.
- Explain why L1's real image becomes L2's real OBJECT — the second lens doesn't care that its 'object' is actually an image formed by the first lens; it just images whatever light rays reach it.
5 · Extend
- When the object sits at L1's 2f point (d_o1 = 20 cm, so d_i1 = 20 cm too), the system magnification comes out to exactly 1 — the final image is the same size and orientation as the original object, even though it passed through two separate inversions. Explain why two inversions (one per lens) cancel out to give an upright-equivalent final orientation... or do they? Check your sign.
- Multi-lens relay systems like this are used in endoscopes and periscopes to transport an image over a distance without losing size or clarity. Explain why a single very-long-focal-length lens couldn't achieve the same compact relay.
The Physics Behind This Experiment
Compound System Magnification
For any chain of imaging elements, the overall system magnification is the product of each individual element's magnification: M = m₁ × m₂ × ... Each element images whatever object (real or the previous element's image) it actually receives.