Describe any two characteristic feature which distiguish interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double slit experiment.
(b) In the diffration due to single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm in incident normally on the slit, calculate the separation in between the first order minima and the `3^("rd")` order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.

Explanation

Expression for internsityh at a point (Y.D.S.E).
Let we have two slits `W_(1) " and "w_(2)` and S be the screen. The displacement due to wave `W_(1) " and "w_(2)` on the screen.
`y_(1)="a sin wt ...(1)"`
`y_(2)="b sin "(omegat+phi)" ...(2)"`
According to the principle os super position, net displacement.
`y=y_(1)+y_(2)`
`y=asin omegat+bsin(omegat+phi)`
`y=a sin omegat+bsinomegatcosphi+b cos omegat sin phi`
`y=sinomegat(a+bcosphi)+cosomegat(bsinphi)`
`"Put,"a+bcosphi=Rcostheta" ....(3)"`
`"and, "bsinphi=Rcostheta" ....(4)"`
`y=Rsinomegatcostheta+Rcosomegatsintheta`
` y=R(sinomegat+theta)`
The resultant wave is harmonic wave of amplitude R.
Squaring and adding equation (3) and (4)
`R^(2)=a^(2)+b^(2)+2abcostheta`
`"where, "I_(1)=Ka^(2),I_(2)=Kb^(2)" and "I_(R)=KR^(2)`
Separation between `3^("rd")" and "I^("st")` order minima
`x_(3)-x_(1)=(3lamdaD)/d=(lamdaD)/d=(2lamdaD)/d=(2xx620xx10^(-9)xx1.5)/(3xx10^(-3))=620xx10^(-6)=6.20xx10^(-4)m`
Hence,
`I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi`
`d=3mm=3xx10^(-3)m`
`D=1.5m`
`lamda=620nm=620xx10^(-9)m`
Position of `3^("rd")` order minima `=(3lamdaD)/d`
Position of 1st order minima `=(lamdaD)/d`