Combined Mirrors and Autocollimation
For coaxial or facing mirrors, apply reflection at each surface with signed coordinates. In autocollimation, placing an object at a converging element's focus returns parallel rays that retrace after plane reflection.
Why this shows up in the exam
Autocollimation · Cassegrain-type paths · Focal-length comparison experiments
Learn the idea
Successive mirrors must be handled in order, with each intermediate image becoming the next object. An optical system passes an image from one element to the next like a relay; coincidence conditions can send rays back to the starting point.
🧠 Memory hook: Image from one surface is object for the next.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- 1/f_j = 1/v_j + 1/u_j — apply separately at each spherical mirror
- u_next = x_image - x_next — signed coordinate transfer between elements
How to approach it
- 1Set one coordinate axis
- 2Process surfaces in encounter order
- 3Use the intermediate image coordinate for the next object
Common slip-ups that cost marks
- •Using one formula for the whole system
- •Losing the direction of light after reflection
- •Ignoring a coincident-image constraint
🌟 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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