Light: Reflection and Refraction

Light travels in straight lines in a uniform medium (rectilinear propagation). A ray shows its path; a bundle of rays is a beam.

Laws of reflection: (1) angle of incidence = angle of reflection, (2) incident ray, reflected ray and normal lie in the same plane. These hold for plane AND curved mirrors.

Plane mirror image: virtual, erect, same size, laterally inverted, and as far behind the mirror as the object is in front.

Spherical mirror terms: pole (P), centre of curvature (C), radius of curvature (R), principal axis, principal focus (F), focal length (f). Key relation: R = 2f.

Concave mirror converges light. Object beyond F gives a real, inverted image; object between P and F gives a virtual, erect, magnified image — that is how dentists and make-up mirrors work.

Uses of concave mirrors: torches, vehicle headlights, shaving mirrors, dentists' mirrors, solar furnaces.

Convex mirror diverges light and ALWAYS forms a virtual, erect, diminished image with a wide field of view — used as vehicle rear-view mirrors.

Refraction is the bending of light when it changes medium, caused by the change in the speed of light. Into a denser medium it bends towards the normal; into a rarer medium, away from the normal.

Rectangular glass slab: light bends at both faces; the emergent ray is parallel to the incident ray but laterally displaced.

Laws of refraction: (1) incident ray, refracted ray and the normal lie in the same plane; (2) sin i / sin r is constant for a given pair of media and for light of a given colour — Snell's law. The constant is the refractive index n21. Absolute refractive index n = c/v; higher n = optically denser = slower light.

Convex lens (thicker middle) converges rays through its optical centre O and foci F1, F2. Image cases: beyond 2F1 → between F2 and 2F2 (real, inverted, diminished); at 2F1 → at 2F2 (real, inverted, same size); between F1 and 2F1 → beyond 2F2 (real, inverted, enlarged); at F1 → at infinity; between O and F1 → virtual, erect, enlarged (magnifying glass!).

Concave lens ALWAYS forms a virtual, erect, diminished image between F1 and the optical centre O, whatever the object position.

Ray-diagram construction rays (any two locate the image): (1) ray parallel to the principal axis passes through F after reflection/refraction; (2) ray through C (mirror) or through O (lens) goes straight, undeviated; (3) ray through/towards F emerges parallel to the axis.

Power of a lens P = 1/f (f in metres), measured in dioptres (D). Convex lens: positive power; concave lens: negative power. Powers of lenses in contact simply add.

Mirror formula

1/v + 1/u = 1/f

u, v, f with New Cartesian signs: distances measured from the pole; real object gives negative u; concave f negative, convex f positive.

Radius of curvature

R = 2f

Focal length is half the radius of curvature (small-aperture mirrors).

Magnification (mirror)

m = h'/h = -v/u

Negative m: real and inverted. Positive m: virtual and erect.

Snell's law

sin i / sin r = n21

n21 = refractive index of medium 2 with respect to medium 1.

Absolute refractive index

n = c / v

c = 3 x 10^8 m/s (speed of light in vacuum), v = speed in the medium. Water 1.33, crown glass ~1.5, diamond 2.42.

Relative refractive index

n21 = n2/n1 = v1/v2

Ratio of speeds in the two media.

Lens formula

1/v - 1/u = 1/f

Note the minus sign — different from the mirror formula. Convex f positive, concave f negative.

Magnification (lens)

m = h'/h = v/u

No minus sign in the lens magnification formula (unlike mirrors).

Power of a lens

P = 1/f (f in metres)

Unit: dioptre (D). 1 D = power of a lens of focal length 1 m. Powers in contact add: P = P1 + P2.