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(a) (i) 'Two independent monochromatic sources of light cannot produce a sustained interference pattern'. Give reason. (ii) Light waves each of amplitude "a" and frequency "omega", emanating from two coherent light sources superpose at a point. If the displacements due to these waves is given by y_(1)=acosomegat and y_(2)=acos(omegat+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 where path difference is lambda//3. |
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Answer» Solution :(a) (i) Light WAVES, originating from two independent monochromatic sources, will not have a constant phase difference. Therefore, these sources will not be coherent and, therefore, would not produce a sustained interference pattern. `(II)` `y=y_(1)+y_(2)` `=acosomegat+acos(omegat+phi)` `=2acos.(phi)/(2).cos(omegat+(phi)/(2))` Amplitude of resultant displacement is `2acos.(phi)/(2)` `:.` Intensity , `I=4a^(2)cos^(2).(phi)/(2)` (b) A path difference of `LAMBDA`, corresponds to a phase difference of `2PI` `:.` The intensity, `K=4a^(2)impliesa^(2)=(K)/(4)` A path difference of `(lambda)/(3)`, corresponds to a phase difference of `(2pi)/(3)` `:.` Intensity `=4a^(2)cos^(2)phi//2` `=4xxa^(2)xxcos^(2).(2pi//3)/(2)` `=4xx(K)/(4)xx((1)/(2))^(2)=(K)/(4)` |
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