Wave Optics: Essential Concepts and Formulas for Class 12 Physics
Wavefront: Wave Optics
The locus of all particles of the medium vibrating in the same phase at a given instant is known as a wavefront. Depending on the shape of sources of light, wavefront can be of three types
Spherical wavefront: When the source of light is a point source, the wavefront is spherical.
Cylindrical wavefront: When the source of light is linear, the wavefront is cylindrical.
Plane wavefront: When the point source or linear source of light is at very large distance, a small portion of spherical or cylindrical wavefront appears to be plane. Such a wavefront is known as plane wavefront.
Huygens principle
According to the Huygens principle, every point on the given wavefront (primary wavefront) acts as a fresh source of new disturbance, called secondary wavelets.
– The secondary wavelets spread out in all directions with the speed of light in the medium.
– A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new (secondary) wavefront at that instant.
Coherent and incoherent sources: The sources of light, which emit continuous light waves of the same wavelength, same frequency and in the same phase or have a constant phase difference are known as coherent sources. Two sources of light which do not emit light waves with a constant phase difference are called incoherent sources.
Interference of light
It is the phenomenon of redistribution of energy on account of the superposition of light waves from two coherent sources. Interference patterns produce points of maximum and minimum intensity. Points, where resultant intensity is maximum, interference, is said to be constructive and at the points of destructive interference, the resultant intensity is minimum.
Conditions for sustained interference of light: The two sources should continuously emit waves of the same wavelength or frequency.
– The amplitudes of waves from two sources should preferably be equal.
– The waves emitted by the two sources should either be in phase or should have a constant phase difference.
– The two sources must lie very close to each other.
– The two sources should be very narrow.
Young’s double-slit experiment:
Young’s double-slit experiment was the first to demonstrate the phenomenon of interference of light. Using two slits illuminated by a monochromatic light source, he obtained bright and dark bands of equal width placed alternately. These were called interference fringes.
Colour of thin films:
A soap film or a thin film of oil spread over water surface, when seen in white light appears colored. This effect can be explained in terms of the phenomenon of interference.
Diffraction of light
It is the phenomenon of bending of light around corners of an obstacle or aperture in the path of light.
Diffraction due to a single slit: The diffraction pattern produced by a single slit of width a consists of a central maximum bright band with alternating bright and dark bands of decreasing intensity on both sides of the central maximum.
The Polarisation of Light
The phenomenon of restricting the vibrations of light (electric vector) in a particular direction, perpendicular to the direction of wave motion is known as the polarisation of light.
Angle of polarisation
The angle of incidence for which an ordinary light is completely polarised in the plane of incidence when it gets reflected from a transparent medium.
Laws of Malus
According to the law of Malus, when a beam of completely plane-polarized light is incident on an analyzer, the resultant intensity of light (I) transmitted from the analyzer varies directly as the square of the cosine of the angle (q) between the plane of transmission of analyzer and polariser
i.e. I ∝ cos2q
Brewster’s law
According to Brewster’s law, when unpolarised light is incident at a polarising angle (ip) on an interface separating a rarer medium from a denser medium of refractive index m, such that m = tan ip then light is reflected in the rarer medium is completely polarised. The reflected and refracted rays are perpendicular to each other.