Saved Bookmarks
| 1. |
Show that the superposition of the waves originating from two coherent sources s_(1) and s_(2) having displacement y_(1)=acosomegat and y_(2)=acos(omegat+phi) at a point produce a result intensity I_(R)=4a^(2)"cos"^(2)(phi)/(2). Hence, write the conditions for the appearance of dark and bright fringes. |
|
Answer» Solution :If two waves are being REPRESENTED as: `y_(1)=acosomegat and y_(2)=acos(omegat+theta)`, then the displacement of resultant wave formed the to their superposition is given by `y=y_(1)+y_(2)=acosomegat+acos(omegat+phi)=2acos((phi)/(2)).cos(omegat+(phi)/(2))` Obviously the AMPLITUDE of the resultant wave is `A=2acos((phi)/(2))` and therefore the resultant intensity at a point will be given by `I_(R)=KA^(2)=k.4a^(2)cos^(2)((phi)/(2))` But `ka^(2)=I=`Intensity of light due to any one superposing wave. so, we have `I_(R)=4Icos^(2)((phi)/(2))`. Condition for bright: If `theta=2npi` (where n=0,1,2,3. . ), then `I_(R)=4Icos^(2)(npi)=4I=`maximum and we obtain bright fringe. Condition for dark fringes: If `phi=(2n-1)pi` (where n=1,2,3. . ), then `I_(R)=4picos^(2)((2n-1)/(2)pi)=0` and we obtain dark fringe. |
|