A Lens Lab That Won't Form a Sharp Image
Students use a converging lens of stated focal length 10.0 cm to form a real image of a lit arrow on a screen. They place the object 15.0 cm from the lens and hunt for the image with a screen, but the sharpest image they can find is at about 27 cm and is noticeably blurry. A second group using the same lens reports a sharp image at 30 cm for the same object distance. The teacher suspects the lens is not actually 10.0 cm, or that the groups are measuring object distance from different reference points. The room has bright overhead lighting, and one group is using a screen with a glossy white finish.
1. Using the thin-lens equation, predict where the image should form for f = 10.0 cm and u = 15.0 cm. Then determine what focal length would be consistent with a sharp image at 30 cm, and interpret the 27 cm result.
Read the worked answer
Prediction with f = 10.0 cm, u = 15.0 cm
1/f = 1/u + 1/v → 1/10.0 = 1/15.0 + 1/v
1/v = 0.1000 − 0.0667 = 0.0333 cm⁻¹ → v = 30.0 cm.
Magnification m = −v/u = −2.0, so the image is real, inverted, and twice the object size.
What f would give v = 30 cm?
1/f = 1/15.0 + 1/30.0 = 0.0667 + 0.0333 = 0.1000 → f = 10.0 cm.
So the second group's 30 cm is exactly the prediction for the stated lens - strong evidence the lens really is 10.0 cm and the second group's geometry is correct.
The 27 cm result
Solving for f with u = 15.0, v = 27.0: 1/f = 1/15 + 1/27 = 0.0667 + 0.0370 = 0.1037 → f ≈ 9.6 cm.
That is only a 4% discrepancy in f but produces a 3 cm shift in v - the image position is very sensitive to f near this configuration, which is itself a useful teaching point. More likely, though, the 27 cm reading is a measurement artifact: a blurry "best focus" judged by eye on a glossy screen under overhead lights is unreliable, and the group may be measuring u from the lens holder rather than the lens centre.
2. List the specific experimental improvements you would direct, and explain which one most likely explains the blur.
Read the worked answer
Improvements, in order of expected impact:
- Fix the reference points. Measure u and v from the lens centre, not the holder edge or the bench clamp. A holder offset of ~1 cm changes v by several cm here.
- Control stray light. Dim the overheads and shield the screen; use a matte screen. A glossy screen under room lights produces glare and a low-contrast image, so "sharpest focus" becomes subjective.
- Use the conjugate-points method rather than a single trial: find two lens positions that both focus the image for a fixed object–screen separation D, then f = (D² − d²)/(4D). This removes reliance on one u value and averages out judgement error.
- Verify f independently by autocollimation or by focusing a distant object (u → ∞ gives v ≈ f).
- Quantify the uncertainty in the best-focus position by having several students judge it independently.
Most likely cause of the blur: the glossy screen plus overhead lighting, which destroys image contrast and makes the focus judgement unreliable. The reference-point error would shift where the sharp image is found; the glare explains why no position looks sharp. Note that this is a hypothesis, not a conclusion - the conjugate-points method would separate the two, since it is insensitive to a single focus judgement.