Optics
Two-lens relay
The first lens makes a real inverted image; the second re-images it. Two inversions cancel to an upright system image.
Trace rays through a compound telescope relay system. Build an astronomical telescope from lenses and observe image formation and angular magnification.
Two-lens relay
The first lens makes a real inverted image; the second re-images it. Two inversions cancel to an upright system image.
The objective lens forms a real intermediate image; the eyepiece or second lens re-images it for the observer. Two inversions yield an upright final image—a standard relay in microscopes and projection systems. Spacing must place the intermediate image at an appropriate conjugate point.
- Two real images
- Overall M = product
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
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?
Predictions to weigh
- System magnification is the sum of the individual magnifications.
- Yes — system magnification is the product of each lens's individual magnification: M = m₁ × m₂.
- System magnification can't be predicted from the individual lens magnifications.
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-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.
Governing equation
Compound System Magnification — M = m₁·m₂·…
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.
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 = 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.
Where this shows up beyond the lab
- 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.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Compound Relay
- Select the first lens
- Press Play
- Two-lens relay
- 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.