(a) Consider two coherent sources S1 and S2 producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by S1 be given by Y1=a cos ωt and the displacement by S2 be Y2=a cos(ωt+ϕ). Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be I=4a2 cos2ϕ2. Hence, establish the conditions for constructive and destructive interference. (b) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slits is increased; (ii) the monochromatic source is replaced by a source of white light.

(a) Consider two coherent sources S1 and S2 producing monochromatic wa

1.	(a) Consider two coherent sources S1 and S2 producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by S1 be given by Y1=a cos ωt and the displacement by S2 be Y2=a cos(ωt+ϕ). Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be I=4a2 cos2ϕ2. Hence, establish the conditions for constructive and destructive interference. (b) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slits is increased; (ii) the monochromatic source is replaced by a source of white light.
Answer» (a) Consider two coherent sources $S_{1}$ and $S_{2}$ producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by $S_{1}$ be given by $Y_{1} = a c o s ω t$ and the displacement by $S_{2}$ be $Y_{2} = a c o s (ω t + ϕ)$ . Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be $I = 4 a^{2} c o s^{2} \frac{ϕ}{2}$ . Hence, establish the conditions for constructive and destructive interference. (b) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slits is increased; (ii) the monochromatic source is replaced by a source of white light.

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