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(a) (i) Two independent monochromatic sources of light cannot produced a sustained interference pattern'. Give reason. (ii) Light waves each of amplitude ''a'' and frequency ''w'', emanating from two coherent light sources superpose at a point. If the displacements due to these waves is given byy_(3)=a cos omega t and y_(2)=a cos(omega t+phi) where phi is the phase difference between the two, obtain the expression for the resultant intensity at the point. (b) In Young's double slit experiment, using monochromatic light of wavelength lambda, the intensity of light at a point on the screen where path difference is lambda, is K units. Find out the intensity of light at a point where path difference is lambda//3. |
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Answer» Solution : The resultant displacement will be GIVEN by `y=y_1+y_2` `=a cos omega t + a cos (omega t+phi)` `=a[cos omegat +acos (omegat+phi)]` `=2acos (phi//12)cos (omegat+phi12)` The AMPLITUDE of the resultant displacement is `2A cos (phi//12)` The INTENSITY of light is directly proportional to the square of amplitude of the wave. The resultant, intensity will be given by `I=4a^2` or `a^2=I/4` |
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