The Focal Point: Where Images Escape to Infinity
1 · Predict
As an object approaches a converging lens's focal length from beyond it, what happens to the image distance?
- The image distance grows without bound, diverging to infinity right as the object reaches the focal point.
- The image distance shrinks toward zero.
- The image distance stays roughly constant.
2 · Set Up
- Open the focal-point preset and press Reset. The lens's focal length is fixed at 10 cm.
- Enable the image-distance readout.
- Set the object distance for each trial (approaching the focal length from beyond it) and record the image distance.
3 · Collect Data
| Object distance d_o (cm) | Image distance d_i (cm) |
|---|---|
| 11 | |
| 10.5 | |
| 10.1 |
Plot image distance d_i (y-axis) against object distance d_o (x-axis) for your three trials. Does it shoot upward as d_o approaches 10 cm?
4 · Analyze
- For one trial, compute d_i = d_o·f/(d_o − f) using f = 10 cm. Compare to the table.
- Explain, using the thin-lens equation, why d_o − f approaching zero (from the positive side) sends d_i toward positive infinity.
5 · Extend
- When the object sits exactly at the focal point, rays leaving the lens emerge perfectly parallel — an image 'at infinity.' Explain why a lighthouse or searchlight places its bulb exactly at the lens's (or mirror's) focal point.
- This exact setup — a source at the focal point producing parallel output rays — is called a collimator, used to create parallel beams for lab instruments. Why might scientists need a beam of perfectly parallel light for certain experiments?
The Physics Behind This Experiment
Thin-Lens Equation Near the Focal Point
As object distance d_o approaches focal length f, the denominator (d_o − f) in d_i = d_o·f/(d_o − f) approaches zero, sending the image distance to infinity — the image 'escapes' to a point at infinity.