Slide 1: Determination of Wavelength of MonoChromatic Light Using Michelson Interferometer M M 1 2 Abhishek A. Gor
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Monochromatic Light : Monochromatic Light A light wave is a harmonic electromagnetic wave.
Light waves having a single frequency and wavelength are called monochromatic light wave.
Coherent Light : Coherent Light Two or more light waves of same frequency maintaining same phase or phase difference are said to be coherent light.
Interference is an important result of superposition of coherent waves.
Superposition of Waves : Superposition of Waves When two or more waves overlap, the resultant displacement at any point and at any instant may be found by adding the instantaneous displacement that would be produced at the point by the individual waves if each were present alone.
It means that the resultant is simply the sum of the disturbance.
Here, in case of electromagnetic waves, the term displacement refers to amplitude of the electric field vector.
Interference : Interference Interference of light is the phenomenon of redistribution of light energy on account of superimposition of light waves from two coherent sources.
e.g.:- colors of oil film floating on the water.
Interference : Interference Mainly there are two types of Interference. 1) Constructive
2)Destructive
Newton’s Rings : Newton’s Rings There is division of amplitude from the incident ray. These two rays are coherent and close to each other and interfere to produce Brightness and darkness.
Condition for Bright and Dark Rings : Condition for Bright and Dark Rings Bright Fringes:
2t=(2m+1)λ/2
Dark Fringes:
2t=mλ
Where,
m=order of fringes
Michelson’s Interferometer : Michelson’s Interferometer
Michelson’s Interferometer : Michelson’s Interferometer
The Optical path of two halves of the incident wave : The Optical path of two halves of the incident wave θ θ d M1 M2’ Incident ray Reflected rays (1) (2) The path difference between two reflected beams = 2d Cosθ = nλ (maxima)
(2n+1)λ/2 (minima)
Determination of Wavelength of monochromatic light : Determination of Wavelength of monochromatic light We have, 2d Cosθ=nλ.
but, at the center θ=0; so that Cos θ=1.
Therefore,
2d=nλ.
If mirror M1 be moved away from M2’ by λ/2, then;
2(d+ λ/2)=nλ+λ
2d+λ=(n+1)λ
Hence (n+1)th fringe now appears at the center.
For the N bright fringes M1 must be moved through Nλ/2.
Suppose during the movement of the M1 through a distance X=X2-X1, N fringes appear at the center of the field.
Thus,
N λ/2=X2-X1
N λ/2=X λ=2X/N
Observation Table : Observation Table The least count is 0.1 μ cm 0.1 × 1 × = 0.1 = 0.1 μ cm
100 100 10000
Calculations : Calculations Wavelength
Probable Error= ΣΙδΙ
10n n=100 rings
Percentage Error=(Probable error)×100 % λ=2X N
Applications : Applications Measurement of wavelength
Determination of the difference in the wavelength of two waves
Thickness of thin transparent sheet
Determination of the refractive index of gases
Standardization of the meter
Questions : Questions
Slide 18: -Abhishek Gor