Ray Optics & Lenses
Trace light rays through lenses and mirrors. Adjust focal lengths, object distances, and see image formation live.
Reflection: angle of incidence = angle of reflection. Both measured from the normal.
Refraction: Snell's law — n₁ sin θ₁ = n₂ sin θ₂. Light bends toward normal when entering a denser medium.
Total internal reflection occurs when light goes from denser to rarer medium at angle > critical angle (sin θc = n₂/n₁).
Mirror equation: 1/f = 1/v + 1/u. Sign convention: distances are measured from the pole.
Lens equation: 1/f = 1/v − 1/u (thin lens formula).
Magnification: m = v/u (mirrors) or m = v/u (lenses). Negative m means inverted image.
Lensmaker's equation: 1/f = (n−1)(1/R₁ − 1/R₂) for a thin lens in air.
Power of a lens: P = 1/f (in diopters when f is in meters). Converging lens: +P, diverging: −P.
Mirror Equation
Relates focal length, image distance, object distance.
Lens Equation
Thin lens formula (with sign convention).
Snell's Law
Law of refraction at interface.
Critical Angle
Angle for total internal reflection.
Magnification
Ratio of image to object size.
Lens Power
Power of lens when f is in meters.
For concave mirrors: real images (inverted) when object is beyond F; virtual image (erect) when object is between F and pole.
Convex mirrors always form virtual, erect, diminished images — used as rear-view mirrors.
Total internal reflection is the basis of optical fibers and the sparkle of diamonds.
A convex lens can act as converging (when n_lens > n_medium) or diverging (when n_lens < n_medium).
For combination of thin lenses in contact: 1/f = 1/f₁ + 1/f₂.
In JEE, master the sign convention first — most errors come from wrong signs, not wrong formulas.