Spherical-Mirror Geometry and Focal Length
For paraxial rays of a spherical mirror, the principal focus lies midway between pole and centre of curvature; focal length is unaffected by the surrounding transparent medium.
Why this shows up in the exam
Reflecting telescopes · Headlamp reflectors · Concave-mirror focal-length experiments
Learn the idea
A paraxial spherical mirror has focal length equal to half its radius of curvature. Near-axis rays see a spherical mirror almost like many tiny tilted plane mirrors and meet near a common focus.
🧠 Memory hook: Mirror focus is halfway to the centre of curvature.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- f = R/2 — paraxial spherical mirror in any uniform surrounding medium
How to approach it
- 1Identify pole and centre of curvature
- 2Apply f = R/2 with the chosen sign convention
- 3Check whether paraxial approximation is intended
Common slip-ups that cost marks
- •Changing mirror focal length on immersion
- •Using diameter instead of radius of curvature
- •Applying the paraxial result to large-aperture marginal rays
🌟 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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