Overview
This lecture covers the key properties, equations, and image characteristics for mirrors and lenses, with a focus on what is most frequently tested on the MCAT.
Mirrors
- Mirrors reflect light; they do not refract light.
- Two types: concave (converging) mirrors make reflected rays meet at a focal point, convex (diverging) mirrors make rays spread apart.
- Mirror shape: concave is like a cave (inward), convex is outward or belly-shaped.
- Each mirror has a focal length (f) and a center of curvature (C); radius of curvature (R) is distance from center to mirror.
- For mirrors: (2R = 1/f) and (R = 1/(2f)).
Lenses
- Lenses refract light, causing rays to bend and pass through to form images on the opposite side.
- Convex lenses are converging (bring rays together), concave lenses are diverging (spread rays apart); these are opposite to mirrors.
- Focal length (f) is positive for converging (convex) lenses, negative for diverging (concave) lenses.
- Object distance (do) is usually positive on the MCAT.
- Images form on the side opposite the object.
Key Equations
- Thin lens equation (applies to both mirrors and lenses): (1/f = 1/do + 1/di), where do = object distance, di = image distance.
- Magnification equation: (M = -di/do).
- Image height to object height ratio: (hi/ho = di/do).
Image Characteristics
- Positive di = real image (opposite side of lens from object); negative di = virtual image (same side as object).
- For converging (convex) lens: usually forms real, inverted images (IR mnemonic).
- For diverging (concave) lens: always forms virtual, upright images (UV mnemonic).
- If |M| > 1, image is enlarged; if |M| < 1, image is reduced.
- Heights and distances are directly proportional.
Key Terms & Definitions
- Focal length (f) — distance from lens or mirror to focal point.
- Center of curvature (C) — center of sphere from which the mirror is a section.
- Radius of curvature (R) — distance from mirror's surface to C.
- Converging system — brings light rays together (concave mirror or convex lens).
- Diverging system — spreads light rays apart (convex mirror or concave lens).
- Real image — formed where light actually converges; can be projected.
- Virtual image — formed where light only appears to diverge from; cannot be projected.
Action Items / Next Steps
- Practice drawing ray diagrams for different mirror and lens setups.
- Memorize key equations and mnemonics (IR/UV, hi/ho = di/do).
- Solve practice problems using the thin lens equation and magnification formula.