Engineering Physics

by

BhaskarDepartment of Physics

K L University

Lecture 3 (30 July)

Interference

InterferencePrinciple 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 = y1 + y2

R = y1 - y2

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 timeCoherence 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.

InterferenceYoung’s Double slit Experiment:

In 1801, Thomas Young first demonstrated experimentally the phenomenon of interference of light. The phenomenon is shown in the figure

InterferenceConstructive 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 = nλPhase Difference δ= 2nπ

InterferenceDestructive 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=

InterferenceConservation 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, 2п,

4п, 6п……..

InterferenceYoung’s Experiment Explanation:

PD = | S1A - S2A | = | 5λ - 6 λ | = 1 λ Constructive Interference

InterferenceYoung’s Experiment Explanation:

PD = | S1A - S2A | = | 5λ – 4.5λ | = 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 = mλ where m = 0, 1, 2, 3, 4, ... • Nodal Points: PD = mλ where m = 0.5, 1.5, 2.5, 3.5, ...

InterferenceConstructive 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.

InterferenceDestructive 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.

InterferenceIdeal Real