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(a)(i) Two independent monochromatic sources of light cannot produce a sustained interference because :(1) If the sources are not coherent , they cannot emit waves continuously (2) Independent sources , emit the waves , which don't have same phase or a constant phase difference (ii) given y1=acosωt, y2=acos(ωt+ϕ), by superposition principle , resultant displacement , y=y1+y2, or y=acosωt+acos(ωt+ϕ), or y=2acos(ϕ/2).cos(ωt+ϕ/2), or y=Acos(ωt+ϕ/2), it is an equation of simple harmonic plane progressive wave , whose amplitude is A, here A=2acos(ϕ/2), now intensity is proportional to square of amplitude , therefore I=KA2=4Ka2cos2(ϕ/2), where K is proportionality constant (b) In interference the intensity I at a point is given by , I=Iocos2(π/λ)x, where x=path difference ,λ=wavelength , Io=intensity of central maximum , when x=λ, I=K, K=Iocos2(π/λ)λ, or K=Iocos2π=Io, when x=λ/3, I=I', I=Iocos2(π/λ)λ/3, or I'=Iocos2(π/3)=I0(1/2)2=K/4,