Light & Optics

Light is a form of energy that produces the sensation of sight, and it behaves as a wave that needs no material medium to travel through.

• Light is an electromagnetic wave, so it can travel even through a vacuum (no medium needed).
• Light travels in a straight line — this is called rectilinear propagation of light.
• The speed of light in vacuum is 3×10⁸ m/s (about 3,00,000 km/s) — the maximum possible speed in nature.
• Light slows down in a medium: it is fastest in vacuum/air and slower in water and glass.
• Light shows both wave nature and particle nature — this is its dual nature.
• The tiny packets (particles) of light energy are called photons.
• Light does not need a medium to travel, unlike sound which always needs a medium.

When light falling on a surface bounces back into the same medium, the effect is called reflection — this is why we see most objects and how a mirror works.

• A polished or shiny surface (mirror) reflects light best, while a rough surface scatters it.
• The ray that falls on the surface is the incident ray; the ray that bounces back is the reflected ray.
• The line perpendicular to the surface at the point of incidence is the normal.

• First law: the angle of incidence equals the angle of reflection — ∠i = ∠r.
• Second law: the incident ray, the reflected ray and the normal all lie in the same plane.
• These two laws hold for both plane and curved (spherical) mirrors.

• Regular reflection — from a smooth, polished surface; gives a clear image (e.g. a mirror).
• Diffused (irregular) reflection — from a rough surface; light scatters in all directions, so we see the object but get no image.

A mirror reflects light, and depending on whether its surface is flat or curved it behaves very differently. Curved (spherical) mirrors are of two kinds — concave and convex.

• The image is virtual, erect and of the same size as the object.
• The image is laterally inverted (left appears right) and is as far behind the mirror as the object is in front.
• Uses: looking glass, in periscopes, and in solar cookers/kaleidoscopes.

• A concave mirror curves inward and converges light to a point (the focus).
• It can form both real and virtual images depending on the object's position.
• When the object is very close, it gives a magnified, erect, virtual image — useful as a shaving/make-up mirror.
• Uses: shaving mirror, dentist's mirror, headlights of vehicles, torches, and solar furnaces.
• Concave mirrors are used as reflectors in headlights and search-lights because they throw a strong parallel beam.

• A convex mirror curves outward and diverges light.
• It always forms a virtual, erect and diminished (smaller) image.
• It gives a wider field of view, so more area is seen in a small mirror.
• Uses: rear-view (side) mirror in vehicles, and security mirrors at shops and blind turns.

The kind of image a mirror makes depends on its shape and on where the object is placed in front of it.

• A virtual image cannot be caught on a screen and is formed where rays only appear to meet (always erect).
• A plane mirror and a convex mirror always form virtual images.
• A concave mirror forms a real image for distant objects and a virtual image for very near objects.

• Mirror formula: 1/f = 1/v + 1/u — relates focal length f, image distance v, and object distance u.
• Magnification m = −v/u = height of image ÷ height of object.
• Focal length is half the radius of curvature: f = R/2.

When light passes from one transparent medium into another, it changes direction at the boundary — this bending is called refraction, and it happens because light changes speed.

• Refraction is caused by a change in the speed of light as it moves between media of different densities.
• Going from a rarer to a denser medium (air to glass/water), light bends towards the normal.
• Going from a denser to a rarer medium (glass/water to air), light bends away from the normal.
• A ray hitting the surface straight along the normal (∠i = 0) passes without bending.

• First law: the incident ray, the refracted ray and the normal all lie in the same plane.
• Second law (Snell's law): sin i ÷ sin r = constant — this constant is the refractive index of the second medium with respect to the first.
• n = sin i / sin r — the ratio of the sine of the angle of incidence to the sine of the angle of refraction is fixed for a given pair of media.

The refractive index of a medium tells us how strongly it bends light and how much it slows light down compared with vacuum.

• A higher refractive index means light travels slower and bends more in that medium.
• Refractive index has no unit (it is a ratio of two speeds).
• The refractive index of vacuum is 1 (and air is taken as nearly 1).
• A medium with higher refractive index is optically denser.

Many common sights that seem odd are simply refraction at work, where light bends as it crosses between air, water and glass.

• A coin in a beaker of water appears raised (the water looks shallower than it really is).
• A swimming pool looks shallower than its real depth due to refraction.
• Stars twinkle because of the refraction of starlight through changing layers of the atmosphere.
• Planets do not twinkle because they are closer and act as extended sources, so the flickering averages out.
• The Sun is seen a few minutes before actual sunrise and after actual sunset because atmospheric refraction bends its light over the horizon.
• Letters under a thick glass slab appear raised and slightly displaced.

When light tries to pass from a denser to a rarer medium beyond a certain steep angle, it does not refract out at all but is completely reflected back inside — this is total internal reflection.

• The angle of incidence must be greater than the critical angle for TIR to take place.
• The critical angle is the angle of incidence for which the angle of refraction becomes 90°.
• At TIR, all the light is reflected back into the denser medium and none escapes.
• A higher refractive index means a smaller critical angle (diamond has a very small critical angle, about 24°).

• A mirage on a hot road is caused by total internal reflection of light through hot air layers, making the road look wet.
• Optical fibres carry light signals using total internal reflection, used in fast internet and endoscopy.
• The sparkle (brilliance) of a diamond is due to total internal reflection — its small critical angle traps light inside, which then escapes in flashes.
• Shining (bright) cracks in glass and the brilliance of glass paperweights also arise from TIR.

A lens is a piece of transparent material with curved surfaces that bends light to form images; the two basic kinds bend light in opposite ways.

• It converges (brings together) parallel rays of light to a focus, so it is a converging lens.
• It can form both real and virtual images depending on object position.
• Uses: in a magnifying glass, in cameras, in projectors, in the human eye, and to correct hypermetropia.

• A concave lens is thin in the middle and thick at the edges.
• It diverges (spreads out) parallel rays of light, so it is a diverging lens.
• It always forms a virtual, erect and diminished image.
• Uses: in spectacles to correct myopia (short-sightedness) and in peepholes of doors.

• Lens formula: 1/f = 1/v − 1/u — relates focal length f, image distance v, and object distance u.
• Convex lens has a positive focal length; concave lens has a negative focal length.

The power of a lens measures how strongly it bends (converges or diverges) light — a more curved, shorter-focus lens has greater power.

• The SI unit of power of a lens is the dioptre (D).
• One dioptre is the power of a lens of focal length 1 metre (1 D = 1 m⁻¹).
• A convex lens has positive power (+); a concave lens has negative power (−).
• A shorter focal length means greater power (more strongly converging or diverging).
• The total power of thin lenses in contact adds up: P = P₁ + P₂.

When white light passes through a glass prism it splits into its component colours, because each colour bends by a different amount.

• The band of seven colours obtained is called a spectrum.
• The seven colours in order are VIBGYOR — Violet, Indigo, Blue, Green, Yellow, Orange, Red.
• Different colours bend by different amounts because they travel at slightly different speeds in glass.
• Red light bends (deviates) the least, as it has the longest wavelength.
• Violet light bends (deviates) the most, as it has the shortest wavelength.
• A rainbow is a natural dispersion of sunlight by tiny water droplets in the sky after rain.

When light strikes very small particles in the atmosphere it is thrown off in all directions; this scattering, which is stronger for shorter wavelengths, explains the colours of the sky.

• Shorter wavelengths (blue/violet) scatter much more than longer wavelengths (red) — this is Rayleigh scattering.
• The sky appears blue because blue light is scattered most by air molecules.
• The Sun appears red at sunrise and sunset because its light travels through more atmosphere, so the blue is scattered away and mostly red reaches our eyes.
• The Sun appears white/yellowish at noon because it is overhead and light passes through the least atmosphere.
• Danger signals and brake lights are red because red scatters the least and travels the farthest, so it is seen from a distance.
• Clouds appear white because their large water droplets scatter all colours equally (this is Tyndall scattering, not wavelength-dependent).
• The sky appears dark (black) to astronauts in space because there is no atmosphere to scatter sunlight.

The human eye works like a natural camera, focusing light onto a light-sensitive screen to form the images we see.

• The retina is the light-sensitive screen at the back of the eye on which the image forms.
• The cornea is the transparent front part where most of the bending of light takes place.
• The iris controls the size of the pupil and so the amount of light entering the eye.
• The pupil is the opening that lets light in.
• The power of adjusting the eye lens to focus on near and far objects is called accommodation, done by the ciliary muscles.
• The least distance of distinct vision for a normal eye is 25 cm.
• The far point of a normal eye is infinity.

Sometimes the eye cannot focus images sharply on the retina; these common defects are corrected with suitable spectacle lenses.

• Myopia is corrected by using a concave (diverging) lens.
• Hypermetropia (long-sightedness) — the person can see distant objects but not near ones; the image forms behind the retina.
• Hypermetropia is corrected by using a convex (converging) lens.
• Presbyopia is the weakening of vision with old age, where both near and distant vision blur as the eye lens loses flexibility.
• Presbyopia is corrected by a bifocal lens (concave for distance, convex for near).
• Astigmatism is the uneven curvature of the cornea/lens, causing blurred vision.
• Astigmatism is corrected by a cylindrical lens.

The colour of an object depends on which colours of light it reflects to our eyes, while the rest are absorbed.

• A red object reflects red light and absorbs the rest; a leaf looks green because it reflects green.
• A white object reflects all colours; a black object absorbs all colours (so black bodies heat up most in sunlight).
• The three primary colours of light are Red, Green and Blue (RGB).
• Red, green and blue light combine to give white light.
• The three primary colours of pigments (paints) are different from those of light.
• A coloured object viewed in light of a different colour can look black (e.g. a red flower in green light looks dark).