Part of OP-01 — Ray Optics

Cornell Note — Spherical Mirrors

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CueNotes
Concave mirrorConverging; f < 0; R < 0 (Cartesian). Focus in front of mirror. Used: shaving mirror, solar concentrator, reflector telescope.
Convex mirrorDiverging; f > 0; R > 0 (Cartesian). Focus behind mirror. Used: rear-view mirror (wide field, erect image).
Mirror Formula1/v + 1/u = 1/f. All three distances measured from the pole P.
Object positionAlways on the left (in front of the mirror). u is ALWAYS negative.
Real imagev < 0 (in front of mirror). Actual ray intersection. Can be projected. Always inverted for mirrors.
Virtual imagev > 0 (behind mirror). Extended ray intersection. Cannot be projected. Always erect for mirrors.
m = −v/uNegative sign is MANDATORY for mirrors (unlike lenses). m < 0 → inverted. m > 0 → erect.
f = R/2Valid for both concave and convex mirrors. Both f and R carry the correct sign.
Concave mirror usesHeadlights (searchlights), shaving mirror (virtual erect magnified), solar furnace, ophthalmoscope.
Convex mirror usesRear-view mirror, security mirror, corner reflectors, ATM cameras.

Summary

Spherical mirrors apply the same formula 1/v + 1/u = 1/f, but sign convention is everything. Concave mirror: both f and R are negative; convex: positive. The magnification m = −v/u for mirrors, with the minus sign being non-negotiable. The most common NEET error: using positive f for a concave mirror.

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