Learning Objectives
- Understand reflection of light and image formation by mirrors
- Learn the mirror formula and magnification
- Understand refraction of light through lenses
- Apply lens formula and understand power of a lens
Key Concepts
Reflection of Light
Laws of reflection: (i) Angle of incidence = Angle of reflection (∠i = ∠r). (ii) Incident ray, reflected ray, and normal lie in the same plane.
Spherical Mirrors
Concave mirror: Reflecting surface is on the inner (cave) side. Converges light. Uses: shaving mirrors, headlights, solar furnaces, dentist's mirrors.
Convex mirror: Reflecting surface is on the outer side. Diverges light. Uses: rear-view mirrors in vehicles (wider field of view).
Key terms: Centre of curvature (C), Radius of curvature (R), Pole (P), Principal axis, Focus (F), Focal length (f). Relationship: R = 2f.
Sign Convention (New Cartesian)
All distances measured from the pole. Distances in the direction of incident light are positive. Distances measured against the direction of incident light are negative. Heights above the principal axis are positive; below are negative.
Mirror Formula and Magnification
Mirror formula: 1/v + 1/u = 1/f
where v = image distance, u = object distance, f = focal length.
Magnification: m = -v/u = h'/h
where h' = image height, h = object height. m is negative for real (inverted) images and positive for virtual (erect) images.
Refraction of Light
Laws of refraction: (i) Incident ray, refracted ray, and normal are in the same plane. (ii) Snell's law: n₁ sin i = n₂ sin r, or n₂₁ = sin i / sin r (refractive index of medium 2 w.r.t. medium 1).
Light bends toward the normal when entering a denser medium and away from the normal when entering a rarer medium.
Lenses
Convex lens (converging): Thicker at centre. Real focus. Uses: magnifying glass, camera, eye lens, projector.
Concave lens (diverging): Thinner at centre. Virtual focus. Uses: correcting myopia, peepholes.
Lens Formula and Power
Lens formula: 1/v - 1/u = 1/f
Magnification: m = v/u = h'/h
Power of a lens: P = 1/f (in metres). Unit: dioptre (D).
Convex lens: positive power; Concave lens: negative power.
Summary
Light reflects off mirrors and refracts through lenses following specific laws. Concave mirrors converge light; convex mirrors diverge it. Convex lenses converge light; concave lenses diverge it. The mirror and lens formulae relate object distance, image distance, and focal length. Sign conventions must be consistently applied in all calculations.
Important Terms
- Focal Length
- Distance between the pole/optical centre and the principal focus
- Refractive Index
- Ratio of speed of light in vacuum to speed in the medium (n = c/v)
- Real Image
- Formed by actual convergence of rays; can be obtained on a screen; inverted
- Virtual Image
- Formed by apparent divergence of rays; cannot be obtained on a screen; erect
- Power of Lens
- Reciprocal of focal length in metres; measured in dioptres (D)
Quick Revision
- Mirror formula: 1/v + 1/u = 1/f; Lens formula: 1/v - 1/u = 1/f
- R = 2f for spherical mirrors
- Concave mirror: converges; Convex mirror: diverges
- Convex lens: converges; Concave lens: diverges
- Power P = 1/f (in metres); +ve for convex lens, -ve for concave lens