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### Wave Optics : Part 2

• In Young’s Experiment two parallel and very close slits S1and S2 (illuminated by other another narrow slit) behaves like two coherent sources and produces a pattern of dark and bright bands (interference fringes) on a screen. For a point P on the screen

S2P-S1P≈y1d/D1

Where d is the separation distance between two slits, D1 is the distance between the slits and the screen and y1 is the distance of point P from the central fringe.

• For constructive interference (bright band) , the path difference must be an integral multiple of wavelength λ i.e.,

y1d/D1 = n λ or y1=nD1λ/d

• The separation distance Δy1 between adjacent bright or dark fringes is

Δy1 = D1λ/d

Using this relation we can calculate wavelength λ.

• The colors shown by thin films are due to interference between two beams , one reflected from the top surface of the film and other from the bottom. The path difference between the two may give constructive interference for one color and destructive interference for another. Hence the reflected light is colored.

• Term diffraction refers to light spreading out from narrow holes and slits, and bending around corners and obstacles.

• The single slit diffraction pattern shows the central maximum (θ=0) at angular separation θ=±n λ (n≠0) and secondary maxima at θ=±(n+1/2) λ (n≠0).

• Different parts of the wave front at the slit acts as secondary sources ; diffraction pattern is the result of interference of waves from these sources.

• An aperture of size a sends diffracted light into an angle ≈ λ/a.

• Doppler effect is the shift in frequency of light when there is a relative motion between the source and the observer. It is given by

Δν/ν ≈ vr/c for v/c << 1

Where vr is the radial component of relative velocity v. This effect can be used to measure the speed of an approaching or receding object.

• Polarization specifies the manner in which electric field E oscillates in the plane transverse to direction of propagation of light. If E oscillates back and forth in a straight line , the wave is said to be linearly polarized. If the direction of E changes irregularly then the wave is un-polarized.