Wavefront : The locus of all particles of the medium vibrating in the same phase at a given instant is known as 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 Huygens principle,
>> Every point on given wavefront (primary wavefront) acts as a fresh source of new disturbance, called secondary wavelets.
>> The secondary wavelets spread out in all the 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.
Effect on frequency, wavelength and speed during refraction:
When a wave passes from one medium to another then change in speed v takes place, wavelength λ also changes, whereas its frequency ν remains the same.
Coherent and incoherent sources : The sources of light, which emit continuous light waves of the same wavelength, same frequency and in same phase or having 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 superposition of light waves from two coherent sources. Interference pattern 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, resultant intensity is minimum.
Intensity distribution : If a, b are the amplitudes of interfering waves due to two coherent sources and f is constant phase difference between the two waves at any point P, then the resultant amplitude at P will be
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 monochromatic light source, he obtained bright and dark bands of equal width placed alternately. These were called interference fringes.
For constructive interference (i.e., formation of bright fringes)
where n = 0 for central bright fringe
n = 1 for first bright fringe,
n = 2 for second bright fringe and so on
d = distance between two slits
D = distance of slits from the screen
xn = distance of nth bright fringe from the centre.
For destructive interference (i.e. formation of dark fringes).
For nth dark fringe,
where
n = 1 for first dark fringe,
n = 2 for second dark fringe and so on.
xn = distance of nth dark fringe from the centre
Fringe width : The distance between any two consecutive bright or dark fringes is known as fringe width.
Angular fringe width :
If W1, W2 are widths of two slits, I1, I2 are intensities of light coming from two slits; a, b are the amplitudes of light from these slits, then
** When entire apparatus of Young’s double slit experiment is immersed in a medium of refractive index m, then fringe width becomes
** When a thin transparent plate of thickness t and refractive index m is placed in the path of one of the interfering waves, fringe width remains unaffected but the entire pattern shifts by
This shifting is towards the side in which transparent plate is introduced.
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.
Condition for nth secondary maximum is
Condition for nth secondary minimum is
Width of secondary maxima or minima
Width of central maximum = 2λD/a
Angular fringe width of central maximum = 2λ/a
Angular fringe width of secondary maxima or minima = λ/a