Class 11 Physics — Chapter 303: Optics

Key concepts: Optics (Class 11 Physics)

Light treated as rays: reflection at spherical mirrors with the mirror formula and sign convention, refraction and Snell's law, total internal reflection with its applications, refraction at a spherical surface leading to the lens maker's formula, lens power and combinations, the prism, and the microscope and telescope. Light treated as a wave: Huygens' principle and wavefronts, coherence and interference in Young's double-slit experiment with its fringe width, diffraction at a single slit and the width of the central maximum, how interference differs from diffraction, and polarisation with Malus's and Brewster's laws.

Laws of reflection

The angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal all lie in one plane.

Spherical mirrors

A concave mirror converges light and can form real or virtual images; a convex mirror always diverges and forms only virtual, diminished images.

Sign convention

Distances are measured from the pole, positive along the incident light and negative against it. Nearly every optics error traces back to a sign here.

Mirror formula and magnification

One relation links object distance, image distance and focal length, with magnification −v/u telling you the size and orientation of the image.

Refraction

The bending of light as it crosses into a medium of different optical density, caused entirely by the change in the SPEED of light.

Snell's law

The ratio of the sines of the angles of incidence and refraction is constant, equal to the ratio of refractive indices of the two media.

Refractive index

The ratio of the speed of light in vacuum to that in the medium. It is always greater than one and depends on the wavelength of light.

Total internal reflection

When light travels from a denser to a rarer medium beyond the critical angle, it is completely reflected — no light is refracted at all.

Critical angle

The angle of incidence in the denser medium for which the refracted ray just grazes the surface at 90°. Its sine equals the reciprocal of the refractive index.

Applications of TIR

Optical fibres, the sparkle of a diamond, mirages and the totally reflecting prisms in binoculars all rely on total internal reflection.

Refraction at a spherical surface

Relates object and image distances across a single curved boundary and is the step from which the lens maker's formula is derived.

Lens maker's formula

Gives the focal length from the refractive index and the two radii of curvature, showing how a lens's power depends on both shape and material.

Thin lens formula and magnification

Links object distance, image distance and focal length; the magnification v/u gives the image size and whether it is erect or inverted.

Power of a lens

The reciprocal of focal length in metres, measured in dioptre. Converging lenses have positive power, diverging lenses negative.

Combination of lenses

For thin lenses in contact, powers simply add algebraically — the basis of correcting lenses and of achromatic doublets.

Optical instruments

A simple microscope magnifies with a single converging lens; a compound microscope and a telescope each use an objective and an eyepiece, but with very different focal-length choices.

Huygens' principle

Every point on a wavefront acts as a source of secondary wavelets, and the new wavefront is their common tangent. It explains reflection and refraction geometrically.

Wavefront

The locus of all points vibrating in the same phase. The direction of propagation is always perpendicular to the wavefront.

Types of wavefront

A point source gives spherical wavefronts, a line source cylindrical ones, and a source at effectively infinite distance gives plane wavefronts.

Coherent sources

Two sources with a constant phase difference and identical frequency. Sustained interference is impossible without them, which is why two bulbs never interfere.

Interference of light

The superposition of coherent waves, producing alternating bright and dark fringes. Energy is redistributed, never created or destroyed.

Young's double slit experiment

The classic demonstration of the wave nature of light, producing equally spaced fringes of uniform brightness on a distant screen.

Conditions for bright and dark fringes

A bright fringe forms where the path difference is a whole number of wavelengths, a dark fringe where it is an odd number of half-wavelengths.

Fringe width

The spacing between consecutive bright fringes, λD/d. Widening the slit separation narrows the fringes; using a longer wavelength widens them.

Effect of immersing in a liquid

The wavelength shortens by a factor n inside the medium, so the whole fringe pattern contracts by the same factor.

Diffraction

The bending of light around obstacles or through narrow apertures, appreciable only when the aperture is comparable to the wavelength.

Single slit diffraction

Produces a broad central maximum flanked by much weaker secondary maxima, with minima where a sin θ equals a whole number of wavelengths.

Width of the central maximum

Twice as wide as any secondary maximum and inversely proportional to slit width — narrowing the slit spreads the pattern out.

Interference versus diffraction

Interference fringes are equally spaced and equally bright and come from two sources; diffraction bands are unequal in width and intensity and come from one aperture.

Polarisation

The restriction of the electric field's vibration to a single plane, possible only because light is a TRANSVERSE wave. Sound can never be polarised.

Malus's law

The intensity transmitted by an analyser varies as the square of the cosine of the angle between the transmission axes of polariser and analyser.

Brewster's law

At a particular angle of incidence the reflected light is completely plane polarised, and the tangent of that angle equals the refractive index.