Optics
Lensmaker lens (from radii)
This lens's focal length comes from its surface curvatures and glass index: 1/f = (n−1)(1/R₁ − 1/R₂).
Lensmaker lens (from radii) — interactive Optics simulation. This lens's focal length comes from its surface curvatures and glass index: 1/f = (n−1)(1/R₁ − 1/R₂). Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Lensmaker's equation
This lens's focal length comes from its surface curvatures and glass index: 1/f = (n−1)(1/R₁ − 1/R₂).
The lensmaker's formula 1/f = (n−1)(1/R₁ − 1/R₂) shows focal length arises from curvatures and glass index. This preset builds a lens from explicit radii so you can test how stronger curvature or higher-index glass shortens f.
- 1/f = (n−1)(1/R₁−1/R₂)
- f from curvatures
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 lens's focal length comes from its glass index and the curvature of its two surfaces. Does making one surface flatter (larger radius of curvature) increase or decrease the focal length?
Predictions to weigh
- Increases — a flatter surface (larger radius) bends light less strongly, giving a longer focal length.
- A flatter surface decreases the focal length.
- Surface curvature doesn't affect focal length, only the glass index does.
Variable roles
What you set:
- First surface radius R₁ (cm)
What you measure:
- Focal length f (cm)
How the investigation runs
- Open the lensmaker preset and press Reset. This lens has index n = 1.5, with its second surface radius fixed at R₂ = −20 cm.
- Enable the focal-length readout.
- Set the first surface's radius of curvature for each trial and record the resulting focal length.
Governing equation
Lensmaker's Equation — 1/f = (n−1)(1/R₁ − 1/R₂)
A thin lens's focal length comes directly from its glass index and both surface curvatures: 1/f = (n−1)(1/R₁ − 1/R₂). This is how a lens designer predicts optical behavior from physical manufacturing parameters.
What the printable worksheet asks students to work out
- For one trial, compute f from 1/f = (n−1)(1/R₁ − 1/R₂) using n = 1.5, R₂ = −20 cm. Compare to the table.
- Explain, using the lensmaker's equation, why increasing R₁ (making the first surface flatter/less curved) increases the focal length — a flatter lens bends light less.
Where this shows up beyond the lab
- This lens has R₁ > 0 and R₂ < 0 — both surfaces bulge outward (a biconvex lens), the strongest common converging shape. Explain, using the lensmaker's equation, why a plano-convex lens (one flat side, R = ∞) has a longer focal length than a biconvex lens of the same glass and comparable curvature.
- Eyeglass lens manufacturers choose surface curvatures (not just glass index) to achieve a prescribed focal length while controlling weight and edge thickness. Explain why two different (R₁, R₂) pairs could give the exact same focal length, using the lensmaker's equation's structure.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Lensmaker
- Select the lens
- Press Play
- Curvature sets focal length
- 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.