Refraction at a Spherical Surface
For paraxial rays at a spherical interface, n2/v - n1/u = (n2-n1)/R using one consistent Cartesian sign convention.
Why this shows up in the exam
Corneal imaging · Lens-surface design · Glass-sphere imaging
Learn the idea
A single curved interface relates object and image positions through its radius and the two refractive indices. Curvature makes different surface normals point toward one centre, so a bundle can converge or diverge after refraction.
🧠 Memory hook: One curved surface: index-weighted reciprocals equal surface power.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- n2/v - n1/u = (n2-n1)/R — paraxial refraction from n1 to n2 at radius R
How to approach it
- 1Draw the centre of curvature
- 2Assign n1, n2, u and R
- 3Solve for signed v and interpret
Common slip-ups that cost marks
- •Using the thin-lens formula for one surface
- •Ignoring medium indices
- •Assigning R without locating its centre
🌟 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.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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