Key Points

A wavefront is a surface of constant phase, representing the locus of points that are oscillating in the same phase. For a point source, the wavefronts are spherical, while for a distant source, they are planar.

Every point on a wavefront acts as a source of secondary spherical wavelets. The new wavefront at a later time is the forward envelope or common tangent to all these secondary wavelets.

Using Huygens' principle, the law of reflection can be derived. It demonstrates that the angle of incidence ($i$) is equal to the angle of reflection ($r$).

Huygens' principle explains refraction and derives Snell's law: $n_1 \sin i = n_2 \sin r$. This relationship can also be expressed in terms of wave speeds as $\frac{\sin i}{\sin r} = \frac{v_1}{v_2}$.

When light refracts from one medium to another, its frequency remains constant, but its speed and wavelength change. The relationship is given by $\frac{v_1}{\lambda_1} = \frac{v_2}{\lambda_2} = \nu$.

When two or more waves overlap at a point, the resultant displacement is the vector sum of the individual displacements produced by each wave.

Two sources of light are coherent if they emit waves of the same frequency and have a constant phase difference between them. Stable interference patterns are only produced by coherent sources.

Constructive interference occurs when the path difference between two waves is an integer multiple of the wavelength, $\Delta x = n\lambda$, where $n=0, 1, 2, ...$. This results in maximum intensity.

Destructive interference occurs when the path difference is an odd multiple of half the wavelength, $\Delta x = (n + \frac{1}{2})\lambda$, where $n=0, 1, 2, ...$. This results in minimum (zero) intensity.

For two coherent sources with individual intensity $I_0$, the resultant intensity at a point with a phase difference $\phi$ is given by $I = 4I_0 \cos^2(\frac{\phi}{2})$.

YDSE demonstrates interference of light by using two closely spaced slits illuminated by a single coherent source, producing a pattern of bright and dark fringes on a screen.

The position of the nth bright fringe (maximum) from the central maximum in YDSE is given by $x_n = \frac{n\lambda D}{d}$, where D is the screen distance and d is the slit separation.

The position of the nth dark fringe (minimum) from the central maximum in YDSE is given by $x_n = (n + \frac{1}{2}) \frac{\lambda D}{d}$.

Diffraction is the phenomenon of bending of light waves around the edges of an obstacle or aperture, causing the light to spread into the geometrical shadow region.

In single-slit diffraction, the condition for the nth minimum intensity is given by $a \sin \theta = n\lambda$, where 'a' is the slit width and $n = \pm 1, \pm 2, ...$.

Polarisation is a property of transverse waves, like light, that describes the orientation of their oscillations. It demonstrates the transverse nature of light waves.

A polaroid is a device that produces plane-polarised light. When unpolarised light passes through a polaroid, its intensity is reduced by half.

When plane-polarised light of intensity $I_0$ passes through an analyser, the transmitted intensity is $I = I_0 \cos^2 \theta$, where $\theta$ is the angle between the pass axes of the polariser and analyser.