Question

What is the reason for your answer to the above question? (a) The two sources do not emit light of the same wavelength (b) The two sources emit waves which travel with different speeds (c) The two sources emit light waves of different amplitudes (d) There is not constant phase difference between the waves emitted by the two sources​

Answer 1

Answer:

(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=Iocos