Light: Reflection, Refraction and the Eye

Nature of light

Light is an electromagnetic wave that needs no medium. Its speed in vacuum is 3 x 10^8 m/s. It travels in straight lines (rectilinear propagation), which explains shadows, eclipses and the pinhole camera.

• Luminous objects give their own light (Sun, stars, bulb); non-luminous objects are seen by reflected light (Moon).
• Transparent (glass, clear water), translucent (butter paper, frosted glass) and opaque (wood, metal) objects pass all, some or no light.
• Time taken by light: Sun to Earth about 8 minutes 20 seconds; Moon to Earth about 1.3 seconds.

Reflection

Laws: (1) the angle of incidence = angle of reflection; (2) the incident ray, reflected ray and normal lie in the same plane.

• Plane mirror image: virtual, erect, same size, laterally inverted, as far behind as the object is in front.
• Regular reflection (smooth surface) gives clear images; diffuse reflection (rough surface) scatters light.
• Two mirrors at angle theta give 360/theta - 1 images; parallel mirrors give infinite images; kaleidoscope uses this.

Spherical mirrors

• Focal length f = R / 2 (R is the radius of curvature).
• Mirror formula: 1/v + 1/u = 1/f. Magnification m = h'/h = - v/u.
• Sign convention: distances measured from the pole; in the direction of incident light = positive; focal length of a concave mirror is negative, of a convex mirror positive.
• Concave mirror images: object beyond C gives a real, inverted, smaller image; object between P and F gives a virtual, erect, enlarged image (shaving mirror).

Refraction

Light bends when it passes from one medium to another because its speed changes.

• Denser to rarer: bends away from the normal. Rarer to denser: bends towards the normal.
• Snell's law: sin i / sin r = n (constant). Refractive index n = c / v; higher n means light slows more (optically denser).
• Examples: a pencil appears bent in water, a pool seems shallower, stars twinkle, a rainbow.
• Total internal reflection: when light goes from a denser to a rarer medium at an angle larger than the critical angle, it reflects fully. Used in optical fibres, endoscopes, diamonds' sparkle, and in mirages.

Lenses

• Lens formula: 1/v - 1/u = 1/f. Magnification m = v/u.
• Power of a lens P = 1/f (f in metres). Unit: dioptre (D). Convex lens: positive power; concave: negative.
• The combined power of lenses in contact is the sum.

Human eye

• Image on the retina is real and inverted; the brain makes it erect.
• Least distance of distinct vision is 25 cm (near point). The far point is infinity.
• Persistence of vision: the image stays on the retina for about 1/16 second; cinema depends on it.
• Blind spot: the point where the optic nerve leaves the retina; no rods or cones.

• Colour blindness is the inability to distinguish colours (often red and green); it is genetic.
• Night blindness is caused by Vitamin A deficiency.
• Eye donation: only the cornea is used.
• Braille is the reading system for the visually impaired (invented by Louis Braille).

Dispersion, scattering and natural effects

• Dispersion: white light splits into seven colours by a prism: VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red). Red bends least, violet most. Newton showed it.
• Rainbow: dispersion, refraction and internal reflection by water drops; seen when the Sun is behind the observer.
• Scattering: the blue sky is because blue light is scattered most (Rayleigh scattering). Red has the longest wavelength and scatters least, so it is used for danger signals. The Sun looks red at sunrise and sunset because light travels a longer path and the blue is scattered away.
• Twinkling of stars is due to atmospheric refraction. Planets do not twinkle because they are close and appear as extended sources.
• Advanced sunrise and delayed sunset (about 2 minutes) are due to refraction.
• Primary colours of light: red, green, blue. Secondary: cyan, magenta, yellow. Primary pigments: cyan, magenta, yellow (printing). Black = no light; white = all colours.
• Colour of an object is the colour it reflects.