Coherent Sources

Wavefront splitting Interferometer

Young’s Double Slit Experiment

Young’s double slit © SPK

Path difference:

For a bright fringe, For a dark fringe, m: any integer

For two beams of equal irradiance (I 0 )

Visibility of the fringes (V) Maximum and adjacent minimum of the fringe system

Photograph of real fringe pattern for Young’s double slit

The two waves travel the same distance –Therefore, they arrive in phase S S'S'

The upper wave travels one wavelength farther –Therefore, the waves arrive in phase S S'S'

The upper wave travels one-half of a wavelength farther than the lower wave. This is destructive interference S S'S'

Young’s Double Slit Experiment provides a method for measuring wavelength of the light This experiment gave the wave model of light a great deal of credibility. Uses for Young’s Double Slit Experiment

Wavefront splitting interferometers Young’s double slit Fresnel double mirror Fresnel double prism Lloyd’s mirror

Confocal hyperboloids of revolution in 3D S S Path difference -confocal hyperbolae with S and S as common foci  =m

Transverse section –Straight fringes S S d P D O x

The distance of m th bright fringe from central maxima Fringe separation/ Fringe width

Longitudinal section –Circular fringes P O rnrn S S d D N 

Path difference = d For central bright fringe

Radius of nth bright ring For small  m

Wavefront splitting interferometers Young’s double slit Fresnel double mirror Fresnel double prism Lloyd’s mirror

Interference fringes Real Virtual Localized Non-localized

Localized fringe  Observed over particular surface  Result of extended source

Non-localized fringe  Exists everywhere  Result of point/line source

Concordance

Discordance = (q+1/2)

Division of Amplitude

Phase Changes Due To Reflection An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling –Analogous to a reflected pulse on a string μ1 μ1 μ2 μ2

Phase shift

D nfnfnfnf n1n1n1n1 n2n2n2n2 B d A C tttt iiii tttt tttt A B C D

Optical path difference for the first two reflected beams

Condition for maxima Condition for minima

Fringes of equal thickness Constant height contour of a topographial map

Wedge between two plates 1 2 glass glass air D t x Path difference = 2t Phase difference  = 2kt -  (phase change for 2, but not for 1) Maxima 2t = (m + ½) o /n Minima 2t = m o /n

Newton’s Ring Ray 1 undergoes a phase change of 180  on reflection, whereas ray 2 undergoes no phase change R= radius of curvature of lens r=radius of Newton’s ring

Reflected Newton’s Ring

Newton’s Ring

1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP