by Bhaskar Department of Physics K L University

Lecture 3 (30 July) Interference

Principle of superposition: This principal states that the resultant displacement of a particle of the medium accepted upon by two or more waves simultaneously is the algebraic sum of the displacements of the same particle due to individual waves, in the absence of the others. If the two displacements are in same direction, the instantaneous resultant displacement due to two waves acting together is expressed as If the two displacements are in opposite directions, the instantaneous resultant displacement due to two waves acting together is expressed as R = y 1 + y 2 R = y 1 - y 2

Interference Conditions for Interference: Coherent Constant Phase difference Constant wavelength and time period Interference of light: when two light waves superimpose, then the resultant amplitude (or Intensity) in the region of superposition is different then the amplitude (or Intensity) of individual waves. This modification in the disturbance of intensity in the region of superposition is called Interference. Constructive Interference Destructive Interference

Coherence and Monochromatic No coherence between two light bulbs Coherence time Coherence length Some later time or distance coherence - two or more waves that maintain a constant phase relation. monochromatic - a wave that is composed of a single frequency and wavelength. Heisenberg uncertainty relation. Interference The two sources which maintain zero or any constant phase relation between themselves are known as coherent.

Interference Young’s Double slit Experiment: In 1801, Thomas Young first demonstrated experimentally the phenomenon of interference of light. The phenomenon is shown in the figure

Interference Constructive Interference: During the interference, when the resultant amplitude is the sum of the amplitudes due to two waves, the interference is known as Constructive Interference. Path Difference = nλ Phase Difference δ= 2nπ

Interference Destructive Interference: During the interference, when the resultant amplitude is equal to the difference of two amplitudes, the interference is known as Destructive Interference. Path Difference = Phase Difference δ=

Interference Conservation of energy during Interference:  Energy cannot be created or destroyed. In the interference the intensity distribution is also can not be destroyed at п, 3п, 5п, 7п………  This can added to the intensity peaks located at 0, 2 п, 4п, 6п……..

Interference Young’s Experiment Explanation: PD = | S 1 A - S 2 A | = | 5 λ - 6 λ | = 1 λ Constructive Interference

Interference Young’s Experiment Explanation: PD = | S 1 A - S 2 A | = | 5 λ – 4.5 λ | = 0.5 λ Destructive Interference

Interference  A representative two-point source interference pattern with accompanying order numbers (m values) is shown below. Path Difference = m λ

Interference Antinodes Points: PD = m λ where m = 0, 1, 2, 3, 4,... Nodal Points: PD = m λ where m = 0.5, 1.5, 2.5, 3.5,...

Interference Constructive Interference: At the point where crest due to one wave meets with the crest due to another wave (or trough with trough), the resultant intensity ( ) at that point increased. These is known as constructive interference.

Interference Destructive Interference: At the point where crest due to one wave meets with the trough due to another wave (or vice versa), the resultant intensity ( ) at that point decreases. These is known as Destructive interference.

Interference When two light wave having different frequencies and varying phase difference, we get un-sustained interference pattern i.e., bright and dark bands cannot be seen. When two light waves having equal frequencies and constant phase difference, then we get sustained interference pattern. i.e we get alternative bright and dark fringes. Here the bright fringe becomes very bright and dark fringe becomes very dark.

Interference To get sustained interference light waves has to be satisfying the following conditions. Conditions for sustained or Good interference pattern: We require two monochromatic light sources. These two sources must be coherent i.e., they constant phase difference. The frequency must be the same. The amplitude must be the same. They must travel in the same directions. These two sources must be as near as possible and the screen must be as far from them as possible.

Interference Ideal Real