Optics: Reflection, Refraction, Lenses, Mirrors, Dispersion and Wave Optics
Optics is the branch of physics that studies the nature, propagation and behaviour of light, and its interaction with matter. It explains why we see our face in a mirror, why a pencil appears bent in a glass of water, why a diamond sparkles, why a rainbow forms after rain, and how a telescope reveals distant planets. Light is an electromagnetic wave that travels in vacuum with a constant speed of about 3 times 10 to the power 8 metres per second, and it also behaves as a stream of particles called photons. This dual nature is central to modern physics.
For candidates preparing for competitive examinations in Assam, including APSC, ADRE, SSC, Railways, NEET and JEE, optics is a high-yield topic. Questions range from simple numericals on mirrors and lenses to conceptual questions on dispersion and the wave nature of light. A strong grasp of the formulas, sign conventions and everyday applications can secure many marks with little risk of confusion. This article is a complete deep-study revision covering every essential idea of ray optics and wave optics in a logical order.
Basic Terms
- Ray of light: the straight-line path along which light travels in a homogeneous medium.
- Beam of light: a bundle of rays. It may be parallel, convergent or divergent.
- Reflection: the bouncing back of light into the same medium after striking a polished or smooth surface.
- Refraction: the bending of light as it passes from one transparent medium into another because its speed changes.
- Refractive index: the ratio of the speed of light in vacuum to its speed in a medium, n = c/v. It has no unit.
- Lens: a transparent refracting medium bounded by two surfaces, at least one of which is curved.
- Focal length: the distance between the optical centre of a lens or mirror and its principal focus.
- Dispersion: the splitting of white light into its component colours when it passes through a prism.
- Dispersion medium: a medium through which light passes, such as water, glass or air; its optical density decides the extent of bending.
Core Concepts and Formulas
- Laws of reflection: the angle of incidence equals the angle of reflection, and the incident ray, the reflected ray and the normal all lie in the same plane.
- Mirror formula: 1/v + 1/u = 1/f, where u, v and f are measured using the Cartesian sign convention. For a spherical mirror, f = R/2.
- Magnification of a mirror: m = h prime / h = minus v / u.
- Snell's law of refraction: n1 sin i = n2 sin r, where i is the angle of incidence and r is the angle of refraction.
- Refractive index: n = c / v = real depth / apparent depth.
- Critical angle and total internal reflection: sin C = 1 / n, valid when light travels from a denser to a rarer medium.
- Lens formula: 1/v minus 1/u = 1/f. Magnification of a lens: m = v / u.
- Lens maker's formula: 1/f = (n minus 1) times (1/R1 minus 1/R2).
- Power of a lens: P = 1/f in metres, measured in dioptres (D). For lenses in contact, P = P1 + P2.
- Prism relation: n = sin[(A + Dm)/2] divided by sin(A/2), where A is the angle of the prism and Dm is the angle of minimum deviation.
- Fringe width in Young's double-slit experiment: beta = lambda D / d, where lambda is the wavelength, D the distance to the screen and d the slit separation.
The Nature of Light
Light carries energy and travels in straight lines in a homogeneous medium. Its speed in vacuum is a universal constant, c = 3 times 10 to the power 8 m/s. Newton proposed a corpuscular (particle) theory, while Huygens proposed a wave theory; later experiments on interference and diffraction established the wave nature, and the photoelectric effect established the particle nature. The wavelength of visible light lies roughly between 400 nanometres (violet) and 700 nanometres (red). Colour is related to wavelength, and frequency is inversely proportional to wavelength, since speed equals frequency times wavelength.
Reflection and Spherical Mirrors
When light strikes a smooth surface it reflects according to the two laws stated above. A plane mirror forms a virtual, erect image of the same size as the object, located as far behind the mirror as the object is in front, and laterally inverted. Spherical mirrors may be concave (converging) or convex (diverging). A concave mirror can form real or virtual images depending on the position of the object, while a convex mirror always forms a virtual, erect and diminished image and gives a wide field of view, which is why it is used as a rear-view mirror in vehicles.
Important uses include a concave mirror as a shaving mirror, in headlights and in dentists' equipment; and a convex mirror in shops and on dangerous road bends. The mirror formula and the sign convention must be applied carefully. Distances measured in the direction of the incident light are taken as positive, and those measured against it as negative; for a concave mirror f is negative and for a convex mirror f is positive.
Refraction and Total Internal Reflection
Refraction occurs because light travels at different speeds in different media. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media. When light passes from a rarer medium such as air into a denser medium such as glass or water, it bends towards the normal and slows down; on passing from denser to rarer it bends away from the normal and speeds up. A familiar example is the apparent bending of a stick partly dipped in water.
When light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle, the light is completely reflected back into the denser medium; this is total internal reflection. Its applications include optical fibres used in communication and in medical endoscopes, the shining of diamonds, the mirage seen on hot roads, and the sparkling of a prism. The critical angle for glass with respect to air is about 42 degrees, and for water about 49 degrees.
Lenses and Their Formulas
A convex lens is thicker at the centre and converges parallel rays to the principal focus; a concave lens is thinner at the centre and diverges them. The lens formula relates the object distance, the image distance and the focal length, and the magnification tells us the size and orientation of the image. A convex lens forms a real, inverted image for objects beyond the focal length and a virtual, magnified image when the object is within the focal length, as in a magnifying glass. A concave lens always forms a virtual, erect and diminished image.
The power of a lens is the reciprocal of its focal length in metres and is measured in dioptres; a convex lens has positive power and a concave lens has negative power. The lens maker's formula shows how the focal length depends on the refractive index of the material and the radii of curvature of the two surfaces. Combinations of lenses are widely used in cameras, microscopes and telescopes.
Dispersion and the Spectrum
When a narrow beam of white light passes through a triangular glass prism, it splits into a band of seven colours: violet, indigo, blue, green, yellow, orange and red, often remembered by the acronym VIBGYOR. This splitting is called dispersion, and it happens because the refractive index of glass is slightly different for different wavelengths. Violet light is bent the most and red the least, so violet appears at the bottom of the spread and red at the top. The coloured band is called a spectrum.
The rainbow is a natural example of dispersion, refraction and total internal reflection of sunlight by tiny water droplets. The blue colour of the sky is due to the scattering of shorter wavelengths of sunlight by molecules of the atmosphere, a phenomenon explained by Rayleigh scattering. A red sunset results from the longer path that light travels through the atmosphere, which scatters away most of the blue. The formation of a spectrum is also the principle behind a spectrometer used in laboratories.
Optical Instruments
Optical instruments extend the power of the human eye. A simple magnifier uses a convex lens to produce an enlarged virtual image. A compound microscope uses two convex lenses, an objective of short focal length and an eyepiece, to give high magnification of tiny nearby objects. An astronomical telescope uses a large-focal-length objective and a short-focal-length eyepiece to magnify distant objects; its magnifying power is the ratio of the focal length of the objective to that of the eyepiece. A terrestrial telescope adds an erecting lens or a prism to give an upright image.
The human eye is itself an optical instrument with a crystalline lens that focuses light on the retina. The least distance of distinct vision is about 25 centimetres. Short-sightedness (myopia) is corrected using a concave lens, long-sightedness (hypermetropia) using a convex lens, and presbyopia using bifocal lenses. A camera uses a convex lens to form a real, inverted image on a light-sensitive sensor or film.
Wave Optics: Interference, Diffraction and Polarisation
Wave optics treats light as a wave and explains phenomena that ray optics cannot. Huygens' principle states that every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is their envelope. Interference is the superposition of two coherent waves, producing alternate bright and dark fringes. In Young's double-slit experiment, the fringe width depends on the wavelength, the distance to the screen and the slit separation. Constructive interference gives bright fringes and destructive interference gives dark fringes.
Diffraction is the bending of light around the edges of an obstacle or through a narrow slit, which becomes noticeable when the size of the aperture is comparable to the wavelength. Polarisation is the restriction of the vibrations of light to a single plane and proves the transverse nature of light waves. Brewster's law relates the polarising angle to the refractive index by tan theta equals n. These concepts are frequently tested in NEET and JEE through applications such as antireflection coatings and polarising sunglasses.
How Numerical Problems Are Solved
The most important step in optics numericals is the correct use of sign conventions. For mirrors and lenses, distances are measured from the pole or optical centre, and the direction of the incident light is taken as positive. Write down u, v and f with proper signs before substituting into the formula. For refraction, always identify which medium is denser and apply Snell's law with the correct indices. For prism problems, use the minimum deviation relation. For interference, ensure all quantities are in the same system of units, usually SI. Finally, interpret the sign of the magnification: a negative value means a real, inverted image, and a positive value means a virtual, erect image.
Examination Trends
In APSC and ADRE papers, optics questions tend to be factual: the laws of reflection and refraction, the speed of light, uses of mirrors and lenses, and the order of colours in a spectrum. In NEET and JEE, questions combine ray diagrams with formulas, and often test total internal reflection, lens combinations, the human eye and optical instruments. Assertion-reason and statement-based questions are common. Numerical problems on the mirror formula, lens formula, magnification and fringe width appear almost every year, so their practice is essential.
Common Mistakes to Avoid
- Using the wrong sign for u, v or f, which reverses the nature of the image.
- Confusing a real image with a virtual image, or an erect image with an inverted one.
- Forgetting that the refractive index is the ratio of the speed of light in vacuum to that in the medium, and is never less than one.
- Applying the formula for total internal reflection when light passes from a rarer to a denser medium.
- Mixing up the lens formula with the mirror formula; one has a plus sign before 1/u and the other a minus sign.
- Assuming that a convex lens always forms a magnified image, when in fact it can form a diminished real image.
- Writing the order of colours in the spectrum incorrectly; violet deviates the most and red the least.
- Forgetting to convert focal length to metres when calculating the power of a lens in dioptres.
How to Prepare This Topic
- Learn the two laws of reflection and Snell's law first, and practise drawing neat ray diagrams.
- Memorise all the formulas, including the mirror, lens, prism and interference relations, and their sign conventions.
- Solve a large number of numericals, taking special care to assign correct signs to u, v and f.
- Connect each concept with a daily-life application, such as spectacles, rear-view mirrors, rainbows and optical fibres.
- Revise the differences between ray optics and wave optics, and solve previous years' question papers under timed conditions.
Frequently Asked Questions
State the two laws of reflection of light.
First, the angle of incidence is equal to the angle of reflection. Second, the incident ray, the reflected ray and the normal to the surface at the point of incidence all lie in the same plane.
What is the refractive index of a medium?
The refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium, n = c/v. It shows how much the light slows down and bends in the medium, and it has no unit.
What is total internal reflection and when does it occur?
Total internal reflection is the complete reflection of light back into a denser medium when it strikes the boundary with a rarer medium at an angle greater than the critical angle. The critical angle is given by sin C = 1/n. It is the principle behind optical fibres and the sparkle of diamonds.
Why does a prism split white light into seven colours?
Because the refractive index of the prism material is different for different wavelengths, each colour is bent through a different angle. Violet is deviated the most and red the least, so white light spreads into the seven colours of the spectrum, VIBGYOR.
What is the power of a lens and what is its unit?
The power of a lens is the reciprocal of its focal length measured in metres, P = 1/f. Its unit is the dioptre (D). A convex lens has positive power, a concave lens negative power, and for lenses in contact the powers add up.