Light

Nature of light

Light is a form of energy that produces the sensation of sight. It is an electromagnetic wave and shows both wave and particle behaviour (wave–particle duality). It travels in straight lines in a uniform medium (rectilinear propagation — the reason for shadows and eclipses) and needs no medium.

• Speed of light in vacuum $c\approx 3\times 10^8$ m/s (299,792,458 m/s). It is the maximum speed possible.
• Light takes about 8 minutes 20 seconds to reach the Earth from the Sun and about 1.3 seconds from the Moon.
• Light is a transverse wave (it can be polarised). Sound is a longitudinal wave.
• Luminous objects emit light of their own (Sun, stars, lamp); non-luminous objects are seen by reflected light (Moon, planets).
• Transparent (glass, clear water) transmits light; translucent (frosted glass, oiled paper) partly; opaque (wood, metal) blocks it.

Reflection

When light falls on a surface and bounces back, it is reflected.

Laws of reflection:

1. The angle of incidence equals the angle of reflection ($i=r$).
2. The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

Plane mirror

The image is virtual, erect, the same size as the object, at the same distance behind the mirror as the object is in front, and laterally inverted (left–right reversed — the reason ambulance is written reversed). A plane mirror rotated by an angle $\theta$ turns the reflected ray through $2\theta$. To see one's full image, a mirror of half the person's height is enough.

Spherical mirrors

• Concave mirror (converging): reflecting surface curved inward. Convex mirror (diverging): curved outward.
• Terms: pole (P), centre of curvature (C), radius of curvature (R), principal axis, principal focus (F) and focal length (f). For small apertures: $f=\frac{R}{2}$.

Mirror formula:

Magnification: $m=\frac{h^{\prime }}{h}=-\frac{v}{u}$. (Sign convention: distances measured from the pole; taken positive in the direction of the incident light. A concave mirror has negative $f$; a convex mirror has positive $f$.)

A convex mirror always gives a virtual, erect, diminished image between P and F, whatever the object position.

Uses: concave mirrors — shaving mirrors, dentists' mirrors, headlights, reflectors, solar cookers, telescopes (reflecting). Convex mirrors — rear-view mirrors of vehicles (wide field of view, erect image), street lights, security mirrors.

Refraction

Refraction is the bending of light when it passes from one transparent medium to another, because its speed changes.

• Light bends towards the normal when it enters a denser medium (slower) and away from the normal when entering a rarer medium.
• Snell's law: $\frac{\sin i}{\sin r}=n$ (constant for a pair of media), the refractive index.
• Refractive index of a medium $n=\frac{c}{v}$ (speed of light in vacuum / speed in the medium). It is a pure number, at least 1. Typical values: air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42 (highest among common substances; the reason for its brilliance).
• Effects of refraction: a pencil in water appears bent; a pond appears shallower than it is (apparent depth = real depth / $n$); stars twinkle (varying refractive index of the atmosphere); the Sun is seen a little before sunrise and after sunset; a swimming pool looks shallower.
• Lateral shift through a glass slab: the emergent ray is parallel to the incident ray but displaced.

Total internal reflection (TIR)

When light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle $C$, all light is reflected back into the denser medium. The critical angle is given by $\sin C=\frac{1}{n}$ (about 41.8° for glass–air, 48.6° for water–air, 24.4° for diamond–air).

Conditions: light must pass from a denser to a rarer medium, and the angle of incidence must be greater than the critical angle.

Applications and examples:

• Optical fibres (communication, endoscopy) — light is trapped by repeated TIR in a glass or plastic core.
• Mirage (desert, hot roads), shining of air bubbles in water, brilliance of a diamond, totally reflecting prisms (periscope, binoculars), shining of a test tube in water.

Lenses

A lens is a transparent material bounded by two curved surfaces.

• Convex (converging) lens: thicker at the centre; converges parallel rays; real focus.
• Concave (diverging) lens: thinner at the centre; spreads rays; virtual focus.

Lens formula: $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$; magnification $m=\frac{v}{u}$.

Power of a lens: $P=\frac{1}{f}$ (with $f$ in metres). SI unit: dioptre (D). A convex lens has positive power, a concave lens negative. Power of a combination of thin lenses in contact: $P=P_1+P_2$.

A concave lens always forms a virtual, erect, diminished image.

The human eye

• Cornea (transparent front; most of the refraction), aqueous humour, iris (coloured; controls the size of the pupil), pupil, eye lens (adjusts focus), ciliary muscles, vitreous humour, retina (light-sensitive screen with rods for dim light and cones for colour), optic nerve.
• Accommodation is the ability of the eye lens to change its focal length to focus objects at different distances. The near point of a normal eye is 25 cm; the far point is at infinity.
• The image on the retina is real and inverted; the brain interprets it upright. Persistence of vision is about 1/16 of a second (basis of cinema).

Defects of vision

Dispersion, scattering and colours

• Dispersion: splitting of white light into its colours by a prism — VIBGYOR (violet, indigo, blue, green, yellow, orange, red). Violet bends the most and red the least; red has the longest wavelength and violet the shortest. Newton first showed that white light is a mixture of colours.
• Rainbow: formed by refraction, internal reflection and dispersion in raindrops, seen with the Sun behind the observer.
• Scattering: the scattering of light is proportional to $1/{\lambda }^4$ (Rayleigh) — blue is scattered much more than red. Therefore the sky is blue, the Sun looks red at sunrise and sunset (blue scattered away over the long path), danger signals are red (least scattered), and the sky appears dark to an astronaut (no atmosphere).
• Twinkling of stars is due to atmospheric refraction; planets do not twinkle because they are close and are extended sources.

Colours

• Primary colours of light: red, green, blue (RGB). Mixing them gives white. Secondary colours: yellow (R + G), cyan (G + B), magenta (R + B).
• Primary pigments (subtractive): cyan, magenta, yellow (CMY) — used in printing.
• The colour of an opaque object is the colour it reflects; a red rose in green light looks black. A transparent object has the colour it transmits.
• Complementary colours add up to white (e.g. red and cyan).

Optical instruments

Other phenomena

• Interference, diffraction and polarisation confirm the wave nature of light. Young's double-slit experiment shows interference. Polaroid sunglasses reduce glare.
• Photoelectric effect (Einstein, Nobel Prize 1921) demonstrates the particle nature: light consists of photons of energy $E=h\nu$.
• Laser (Light Amplification by Stimulated Emission of Radiation) gives a highly monochromatic, coherent, directional beam; used in surgery, cutting, barcode scanners, communication, holography.
• Raman effect (C. V. Raman, Nobel Prize 1930) is the change in wavelength of scattered light; National Science Day is 28 February.
• Eclipses: a solar eclipse occurs at new moon when the Moon lies between the Sun and the Earth; a lunar eclipse at full moon when the Earth lies between the Sun and the Moon.

Frequently tested facts

• Speed of light ≈ 3 × 10⁸ m/s; sunlight takes about 8 min 20 s to reach the Earth.
• Plane mirror: virtual, erect, same size, laterally inverted; convex mirror in vehicles; concave mirror in headlights and shaving.
• Refractive index $n=c/v$; diamond has the highest among common substances (about 2.42).
• TIR: optical fibres, mirage, diamond's sparkle.
• Power of a lens $=1/f$ (dioptre); convex lens positive, concave negative.
• Myopia → concave lens; hypermetropia → convex lens.
• Red is scattered least and violet most; the sky is blue due to scattering.
• Primary colours of light: red, green, blue.