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Obtain the formula of intensity if the phase difference at a point from two sources is phi. |
Answer» Solution : Suppose point G as shown in figure and let the path difference between TWO displacement be `phi` at that point. If the displacement produced by `S_(1)` at G is `y_(1)=acosomegat` then the displacement produced by `S_(2)` at G would be `y_(2)=ACOS(omegat+phi)`. The resultant displacement according to SUPERPOSITION principle `y=y_(1)+y_(2)=acosomegat+acos(omegat+phi)` `=a[cosomegat+cos(omegat+phi)]` `=2acos""(phi)/(2).cos(omegat+(phi)/(2))` `[:.cosA+cosB=2cos((A+B)/(2))cos((A-B)/(2))]` AMPLITUDE of resultant displacements `=2acos((phi)/(2))` and and intensity of point G, `Iprop4a^(2)cos^(2)""(phi)/(2)` `I=4I_(0)cos^(2)((phi)/(2))""[:."t=where "I_(0)propa^(2)]` If this equation is obeyed, then the CONSTRUCTIVE interference will formed at point G and interference leading to maximum intensity. For maximum intensity from this equation, `phi=0,pm2pi,pm4pi`...... for the value `phi`, then constructive interference will formed and interference leading to maximum intensity. Reverse from this equation, if at point G `phi=pmpi,pm3pi,pm5pi.....,` for the value of o, then destructive interference will formed and leading to zero intensity. |
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