Newtonian Lens Formula and x-y Plot
For a thin lens with Newtonian object and image distances x and y measured from the corresponding focal points under the stated real-conjugate convention, xy = f squared; a plot of y against x is therefore a rectangular hyperbola.
Why this shows up in the exam
Reading focal length from an x-y plot · Checking Newtonian conjugate data · Linearizing data with reciprocal coordinates
Learn the idea
Distances measured from the focal points obey a product equal to the square of focal length. Shifting the origin from the lens to each focal point turns the usual lens formula into a simple rectangular hyperbola, so one plotted coordinate determines the other.
🧠 Memory hook: From the focal points, the two distances multiply to f squared.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- xy = f² — Newtonian form for distances measured from focal points
- f = sqrt(xy) — focal length from any valid plotted conjugate pair
How to approach it
- 1Confirm where x and y are measured from
- 2Choose a clear plotted point
- 3Calculate sqrt(xy) and cross-check another point if visible
Common slip-ups that cost marks
- •Using distances from the lens in xy=f squared
- •Adding x and y instead of multiplying
- •Reading an OCR-damaged graph as verified data
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In a meter bridge, resistance 2 ohm is in the left gap and balance occurs at 40 cm from the left end. Find the right-gap resistance.
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