Overview
This lecture covers the mirror formula, magnification, and the sign convention for spherical mirrors, with examples for both concave and convex mirrors.
Spherical Mirrors and Their Types
- Spherical mirrors are of two types: concave (converging) and convex (diverging).
- Concave mirrors reflect light inward; convex mirrors reflect light outward.
Sign Convention for Spherical Mirrors
- All distances are measured from the mirror's pole (vertex).
- Distances measured in the direction of incident light are positive.
- Distances measured opposite to the direction of incident light are negative.
- For mirrors, object distances (u) are usually negative (object left of mirror).
- For concave mirrors, focal length (f) is negative; for convex mirrors, f is positive.
- Heights above the principal axis are positive; below are negative.
Mirror Formula
- The mirror formula relates object distance (u), image distance (v), and focal length (f):
1/f = 1/v + 1/u
- Used for both concave and convex mirrors by applying proper signs.
Magnification Formula
- Magnification (m) is the ratio of image height (h') to object height (h):
m = h'/h = -v/u
- Negative magnification means the image is inverted; positive magnification means it is erect.
Example Problem (Application)
- Given: Object height = 1 cm, object distance u = -9 cm, concave mirror f = -6 cm.
- Apply mirror formula: 1/f = 1/v + 1/u to find image distance v.
- Calculate magnification using m = -v/u, then find image height h' = m × h.
- Determine if image is real or virtual, magnified or diminished, inverted or erect based on sign and values.
Key Terms & Definitions
- Concave mirror — spherical mirror that converges light, reflective surface curved inward.
- Convex mirror — spherical mirror that diverges light, reflective surface curved outward.
- Pole (P) — central point on the mirror’s surface.
- Principal axis — imaginary line passing through pole and center of curvature.
- Focal length (f) — distance from pole to focus.
- Object distance (u) — distance from object to pole.
- Image distance (v) — distance from image to pole.
- Magnification (m) — ratio of image height to object height.
Action Items / Next Steps
- Practice numericals using mirror and magnification formulas.
- Review sign conventions for different mirror setups.
- Complete textbook exercises on spherical mirrors.