Convex-Lens u-v Relation and Graph
For a thin convex lens forming a real image with consistent sign convention, the measured conjugate distances satisfy 1/f = 1/v - 1/u, or 1/f = 1/v + 1/|u| when positive magnitudes are used.
Why this shows up in the exam
Selecting a correct u-v graph · Estimating focal length from asymptotes · Checking optical-bench observations
Learn the idea
Measured object and image distances for a thin convex lens must satisfy the lens equation and its graph. Moving a real object farther from a convex lens pulls the real image toward the focal plane; the pair of distances traces a hyperbolic relation with focal-length asymptotes.
🧠 Memory hook: Far object, image near f; object near f, image far away.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- 1/f = 1/v + 1/|u| — real-object, real-image magnitude form
- v = f|u|/(|u|-f) — u-v graph for |u| greater than f; asymptotes occur at f
How to approach it
- 1Identify sign or magnitude convention
- 2Test limiting cases near f and infinity
- 3Use one equation point to reject misleading graphs
Common slip-ups that cost marks
- •Mixing signed distances with magnitudes
- •Drawing a straight-line u-v graph
- •Using real-image equations when the object is inside focus
🌟 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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