Ch 6Optics — Class 12 Physics, concept-first.

Light has puzzled physicists for centuries because no single model captures every one of its behaviours.

Ray optics is the branch of optics that represents light as a ray: a straight line showing only the direction light travels in, not its intensity or colour.

Reflection is the bouncing back of light into the same medium when it strikes a reflecting surface. A silvered mirror reflects almost 90% of the light incident on it.

The angle of deviation is the angle between the incident ray's original direction and the direction the light ends up travelling in after reflection.

For a point object placed in front of a plane mirror, a ray strikes the mirror at and reflects along , while a second ray strikes the mirror normally at and reflects straight back along .

A plane mirror's image has four defining characteristics: it is virtual (cannot be projected onto a screen), erect (right-way up), laterally inverted (left and right are swapped, though up and down ar…

A plane mirror does not always form a virtual image. When a real object sends out ordinary divergent rays, reflection off a plane mirror still leaves them divergent, so they only appear to originate f…

A spherical mirror is a curved reflecting surface cut from part of a hollow sphere, usually made from glass with one surface silvered so reflection happens at the other, polished surface.

Rays travelling very close to the principal axis, making only small angles with it, are called paraxial rays; they strike a spherical mirror very close to its pole.

For a concave mirror, a paraxial ray parallel to the principal axis strikes the mirror at and reflects through the principal focus ; the line (through the centre of curvature) is the normal at , and t…

The image formed by a spherical mirror can be located graphically using any two of four standard construction rays, drawn from a point on the object: (i) a ray parallel to the principal axis reflects…

To keep every mirror formula valid for every possible situation, a single Cartesian sign convention is used throughout: (i) incident light is always taken to travel from left to right; (ii) all distan…

The mirror equation relates object distance , image distance , and focal length for any spherical mirror: .

Lateral (transverse) magnification is defined as the ratio of image height to object height, . Applying the Cartesian sign convention to the similar triangles used in deriving the mirror equation give…

Light travels with a very high but finite speed. In vacuum this speed is denoted , with value . Several scientists attempted to measure this speed; the earliest successful terrestrial measurement was…

Fizeau's apparatus for measuring the speed of light in air used a light source , a partially silvered glass plate tilted at to send light out towards a rotating toothed wheel with teeth and equal-widt…

Building on Fizeau's method, later scientists like Foucault (1819-1868) and Michelson (1852-1931) introduced different transparent media -- glass, water, and even evacuated glass tubes -- directly int…

The refractive index of a transparent medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium: .

The optical path of a medium is the distance that light would travel in vacuum in the same time that it actually takes to cross a real distance through that medium.

Refraction is the passage of light from one optical medium into another across a boundary. The angle of incidence (in the first medium) and angle of refraction (in the second medium) are both measured…

The angle of deviation due to refraction is the angle between the incident ray's original direction and the refracted ray's new direction.

Three general characteristics of refraction: (a) light passing from a rarer medium into a denser one deviates towards the normal in the denser medium; (b) light passing from a denser medium into a rar…

The principle of reversibility states that light will follow exactly the same path if its direction of travel is reversed.

In Snell's law, the ratio is called the refractive index of the second medium relative to the first, written .

When viewed from nearly directly above, an object at the bottom of a denser medium (e.g. water) appears closer to the surface than it really is, because light refracting from the denser medium into th…

When light travels from a denser medium (index ) toward a rarer medium (index ), the refraction angle exceeds the incidence angle ; as is increased, grows even faster and reaches exactly (grazing the…

Total internal reflection, once established, produces a wide range of everyday and technological effects, covered one at a time in this subsection: the sparkle of a cut diamond; the mirage (and its re…

Diamond's brilliant sparkle is a direct consequence of total internal reflection. Diamond's refractive index, about 2.417, is far higher than ordinary glass's roughly 1.5, giving diamond a correspondi…

The refractive index of air increases as its density increases. In hot places, air near the ground is hotter (and hence less dense, lower refractive index) than air higher up, so in effect the refract…

Right-angle glass prisms can be used instead of silvered mirrors to reflect light through or through a full , or to invert an image without changing its size, purely by relying on total internal refle…

When a light source such as an electric bulb is placed inside a water tank, light travels outward from it in every direction inside the water.

An optical fibre consists of an inner part called the core, surrounded by an outer part called the cladding (or sleeving); the refractive index of the core material must be higher than that of the cla…

To ensure light entering an optical fibre will be guided by total internal reflection once inside, it must be launched at no more than a maximum incidence angle at the fibre's end face, called the acc…

When a ray of light passes through a parallel-sided glass slab of thickness and refractive index , it refracts twice: entering the slab (rarer air to denser glass) it bends towards the normal, and lea…

Refraction so far has been treated only at flat (plane) boundaries; it also takes place at spherical surfaces separating two transparent media.

For two media of refractive index (containing a point object ) and , separated by a spherical surface of radius of curvature and centre of curvature , a paraxial ray from strikes the surface at and be…

For an extended object refracted at a single spherical surface, forming an image , the lateral magnification can be found using a ray from aimed directly at the centre of curvature -- since this ray m…

A thin lens is formed by a transparent material bounded between two spherical surfaces, or between one spherical and one plane surface, with the separation between the two surfaces small enough to be…

Because a thin lens may separate two different media on its two sides, it has two distinct focal points.

The sign convention for a thin lens's focal length differs from that of a spherical mirror. Because a lens genuinely has two focal points (one on each side), the sign of its focal length is not fixed…

For a thin lens of refractive index in a surrounding medium of index , with radii of curvature for its two surfaces, applying the single-spherical-surface refraction equation once at each surface in t…

For an object of height on the axis, the ray through the lens's own pole travels completely undeviated, creating the similar triangles with the inverted real image of height .

The power of a lens measures how strongly it converges or diverges light, defined as the reciprocal of its focal length, , with SI unit dioptre (D), where .

For two thin lenses of focal length placed in contact at a common optical centre, writing the lens equation once for the first lens () and once for the second, using the first lens's image as the seco…

Two thin lenses of focal length separated by a distance cannot, in general, be replaced by a single equivalent thin lens for an object at a finite distance -- that requires the more involved theory of…

A prism is a triangular block of glass or plastic, bounded by three plane faces that are not parallel to one another.

A ray strikes the first refracting face of a prism at incidence angle , refracting to as it enters the glass; it crosses the prism as , then strikes the second face from inside at , refracting out at…

Plotting the angle of deviation against the angle of incidence for a prism gives a curve that falls to a single minimum value , called the angle of minimum deviation, before rising again on either sid…

At minimum deviation, and ; substituting into gives , i.e. , and substituting into gives . Substituting these into Snell's law gives the prism formula , letting a prism material's refractive index be…

When white light passes through a prism, dispersion occurs -- the splitting of white light into its constituent colours (a spectrum), because the refractive index of the prism material (and hence the…

If are the deviations a prism produces for violet and red light, of refractive indices , then is called the angular dispersion -- the angular gap between the two extreme colours of the spectrum, depen…

When sunlight enters the atmosphere, atmospheric particles change the direction of the light -- a process called scattering.

Light is a form of energy transferred from one place to another, and a glance at the evolution of the various theories put forward by scientists over time to explain it gives an overview not just of t…

Sir Isaac Newton (1672), building on an idea suggested earlier by Descartes (1637), proposed the corpuscular theory: light consists of tiny, essentially massless, perfectly elastic particles called co…

Christian Huygens (1678) proposed the wave theory: light is a disturbance from a source, travelling as a longitudinal mechanical wave through a hypothetical medium called ether, presumed to fill all s…

Maxwell (1864) proved that light is an electromagnetic wave, transverse in nature, carrying electromagnetic energy, and -- crucially -- requiring no medium at all for its propagation.

Albert Einstein (1905), building on ideas put forward by Max Planck (1900), successfully explained the photoelectric effect by treating light as interacting with matter in the form of photons -- discr…

The chapter now turns from ray optics to wave optics: light is a transverse electromagnetic wave, and its wave nature was first demonstrated experimentally through interference and diffraction.

Wave optics studies the wave characteristics of light -- specifically the phenomena of interference, diffraction and polarisation, covered in the remaining sections of this chapter.

The shape of a wavefront depends on the shape of its source and its distance from that source: a point source at a finite distance gives spherical wavefronts; an extended (line) source at a finite dis…

Using Huygens' principle, the law of reflection can be derived directly from wave geometry. A plane wavefront , perpendicular to incident rays , strikes a plane mirror obliquely, so point reaches the…

The same Huygens' construction, applied at a refracting rather than a reflecting boundary, proves Snell's law.

Interference is the phenomenon of superposition (addition) of two light waves, producing an increase in intensity at some points and a decrease at others.

Phase is the angular position of vibration of a wave. In the path of a travelling wave, one full wavelength corresponds to a phase change of exactly , so a general path difference corresponds to a pha…

Two light sources are coherent if they produce waves of the same phase or constant phase difference, the same frequency (monochromatic), the same waveform, and preferably the same amplitude -- coheren…

A double slit uses the principle of wavefront division: two slits , both illuminated by a single monochromatic source , act as a set of coherent sources.

In Young's double-slit experiment, a single monochromatic source illuminates a double slit (separation , both equidistant from , so both are automatically fed in phase), and a screen is placed at dist…

When polychromatic (white) light is used instead of a single wavelength in an interference experiment, coloured fringes of varying width appear on the screen, since different colours have different wa…

A thin transparent film of refractive index and thickness , struck by a parallel beam at (near-)normal incidence, splits the light at its upper surface into a reflected part and a refracted part; the…

Diffraction is bending of waves around sharp edges, into the region that would otherwise be a geometrical shadow -- a general property shared by every type of wave, sound, water and light alike.

Based on the shape of the wavefront undergoing diffraction, diffraction is classified into two types. Fresnel diffraction involves a spherical or cylindrical wavefront, arising when the light source i…

A parallel beam of light falling normally on a single slit of width produces, on a distant screen, a diffraction pattern whose intensity at a general point (making angle with the normal from the slit'…

Considering the first-minimum condition in special cases: (i) if , diffraction cannot occur at all, since can never exceed 1; (ii) if , diffraction is possible -- for exactly, , i.e.

Fresnel's distance is the distance, from a diffracting aperture of width , up to which the rectilinear (straight-line ray) propagation of light remains a good approximation, and beyond which the bendi…

Interference and diffraction are closely related and can be hard to sharply distinguish, since both exhibit the wave nature of light, both involve light reaching geometrically shadowed regions, and bo…

A diffraction grating is a plane sheet of transparent material ruled with a very large number of closely and equally spaced opaque lines (a modern commercial grating has around 6000 lines per centimet…

The wavelength of a spectral line can be measured very accurately using a diffraction grating together with a spectrometer.

When white light is used with a diffraction grating instead of monochromatic light, the diffraction pattern consists of a white central (zero-order) maximum, with continuous, coloured spectra spread o…

Diffraction limits the sharpness of any image formed by a finite-sized aperture. Even a perfect optical instrument images a single point source not as a true point, but as a small bright central disc…

Polarisation is the phenomenon of restricting the vibrations of light (its electric or, equivalently, magnetic field vector -- this chapter only discusses the electric field) to one particular directi…

A transverse wave whose vibrations occur in every direction within the plane perpendicular to its propagation direction is called unpolarised light; these vibrations can always be resolved into two pe…

Unpolarised light can be converted to plane polarised light by four distinct techniques, each covered in its own subsection: (i) polarisation by selective absorption, using dichroic materials such as…

Selective absorption is the property of certain materials that transmit light whose electric field vibrates parallel to one particular direction (the material's own transmission axis) while absorbing…

When unpolarised light passes through a polaroid , its vibrations are restricted to a single plane, emerging as plane polarised light; passing this beam through a second polaroid and rotating about th…

In plane polarised light, the transmitted intensity through a rotating analyser varies all the way from a maximum down to exactly zero, once every of rotation, because the vibrations are fully allowed…

Malus' law: when a beam of plane polarised light of intensity is incident on an analyser, the transmitted intensity varies directly as the square of the cosine of the angle between the transmission ax…

Everyday and technological uses of polaroids: (1) goggles and cameras, to reduce glare; (2) three-dimensional motion pictures (holography-related viewing systems); (3) improving the contrast of old, f…

The simplest method of producing plane polarised light is by reflection. An unpolarised beam incident on a reflecting glass surface splits into a reflected beam and a refracted beam ; examining with a…

In 1808, Malus discovered that ordinary light reflected off a transparent surface is partially plane polarised, with the extent of polarisation depending on the angle of incidence; at one particular a…

The pile-of-plates arrangement exploits polarisation by reflection to build up a strongly polarised beam.

Erasmus Bartholinus, a Danish physicist, discovered that when a ray of unpolarised light is incident on a calcite crystal, it splits into two separate refracted rays, so a single object viewed through…

Not every doubly-refracting crystal has just one optic axis. Crystals possessing only a single optic axis -- the special direction along which the ordinary and extraordinary rays travel at the same sp…

William Nicol (1828) designed the Nicol prism, an optical device used both to produce and to analyse plane polarised light, exploiting the double refraction of a calcite crystal.

The light from a clear blue portion of the sky shows a rise and fall of intensity when viewed through a rotating polaroid, because sunlight scattered by air molecules changes its polarisation state de…

The remaining sections apply every result derived so far -- the mirror and lens equations, magnification, total internal reflection, and diffraction-limited resolution -- to real optical instruments u…

A simple microscope is a single magnifying (converging) lens of small focal length, used to obtain an erect, magnified, virtual image; the object is placed between the pole and the focus of the lens,…

In near point focusing, a simple microscope's object is placed so that the final virtual image forms at the near point, meaning the image distance is (with sign convention) , where is the standard 25…

In normal focusing, the object is placed exactly at the lens's focus, so the image forms at infinity, and no ordinary linear magnification can be meaningfully defined (a linear ratio would itself be i…

The resolving power of a microscope depends not just on its ability to magnify, but on its ability to resolve two points on the object separated by a small distance -- the smaller , the better the res…

A compound microscope uses two lenses: the objective, near the object, forms a real, inverted, magnified image; this image acts as the object for the second lens, the eyepiece, which -- functioning ex…

From the ray diagram, the linear magnification produced by the objective alone is ; using the tube length (the distance between the objective's second focal point and the eyepiece's first focal point)…

An astronomical telescope is used to magnify the apparent size of distant astronomical objects -- stars, planets, the Moon -- and forms an inverted final image.

The magnification of an astronomical telescope is the ratio of the angle the final image subtends at the eye to the angle the object itself subtends at the (unaided) eye or the objective, ; using and…

A terrestrial telescope is used to view objects on the ground, where an erect (rather than inverted) final image is essential.

Modern telescopes use a concave (typically parabolic) mirror rather than a lens as the objective, because manufacturing very large lenses free of optical defects is difficult and expensive; telescopes…

The spectrometer is an optical instrument used to study the spectra produced by different light sources and to measure the refractive indices of materials.

To find the refracting angle of a prism, the prism is placed refracting-edge-first towards the collimator, and its slit, illuminated by monochromatic (e.g.

The eye is a natural optical instrument. As the eye's own lens is flexible, its focal length can be varied to some extent by muscular effort (accommodation): fully relaxed, the focal length is at its…

Myopia (nearsightedness) occurs when the eye lens has too short a focal length, from a thickened lens or an eyeball longer than normal; these people struggle to relax the eye enough (rather than strai…

Hypermetropia (farsightedness, or hyperopia) occurs when the eye lens has too long a focal length, from a thinned lens or an eyeball shorter than normal, so rays from a near object are brought to a fo…

Astigmatism is a defect arising from unequal curvature of the eye's cornea or lens along different planes, so an astigmatic person cannot focus equally sharply on lines running in every direction at o…

This unit developed ray optics from the two laws of reflection through plane and spherical mirrors (mirror equation, magnification, Cartesian sign convention), refraction and Snell's law (apparent dep…

The unit's structure branches into Ray Optics -- reflection and refraction feeding into the spherical mirror (mirror equation, magnification), refraction at a spherical surface feeding into the lens m…

Five sets of practice problems close the unit: Multiple choice questions (20, testing quick recall and short calculations across every topic), Short Answer Questions (80, covering definitions, law sta…

Sample papers and previous-year board questions for this subject.