Chapter 14: Super Position of waves

Principle of superposition of wave
The idea that we can find the resultant of two waves which meet at a point simply by adding up the displacement at each point is principle of superposition. Principle of superposition states that when two waves meet at a point, the resultant displacement is the algebraic sum of displacements of individual waves.

Diffraction
Diffraction is bending of wave as it moves around an obstacle or passes through a narrow opening. The wave will try to curve around the boundary or outward through the opening due to friction.

Interference

Interference is a special case of superposition where the waves that combine are coherent. The waves overlap and form a repeating interference pattern of maxima and minima area. It is the formation of points of cancellation and reinforcement where two coherent wave pass through each other.

Coherence: Waves which are of same frequency, wavelength, polarization and amplitude and in a constant phase relationship. Two sources are coherent when they emit waves with constant phase difference.

Constructive Interference

The path difference between the wave is a whole number of wavelength so the waves arrive in phase adding together to give a large wave.

Path difference = 0, λ, 2λ, 3λ, etc.

Or, path difference = nλ

Destructive Interference

The path difference between the waves is an odd number of half wavelength so wave arrive out of phase cancelling out to give no wave at all.

Path difference = 1/2λ, 3/2 λ, 5/2 λ, etc.

Path difference =(n+1/2 ) λ

Young Double-Slit Experiment

Young’s double slit of interference proves that light is a wave.

Here, the young’s double slit is set up where, the two slits act as coherent source of waves.

Interference occurs where the light from the two slits overlaps. Constructive interference produces bright areas, while deconstructive interference produces dark areas. These area are called interference fringes.

There is a central bright fringe directly behind the midpoint between the slits with more fringes evenly spaced and parallel to the slits. As we move away from the center of the screen we see the intensity of bright fringes decreases.

Observing Diffraction

Observing diffraction with transmission grating:

Monochromatic light from laser is incident normally on a transmission diffraction grating. Interference fringes are formed.

Calculation is done by measuring angle θ at which they are formed, rather than measuring their separation. The central fringe is the zeroth- order maximum (θ = 0) which is bright as all of the rays are travelling parallel to one another.

dsinθ = nλ

Where, d is the distance between adjacent lines and n is the order of maximum. 

Diffracting white light

Diffraction grating is a simple way of separating white light into its constituent wavelengths. Violet is the closest to the center and red is the furthest away.