(i) 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 = acosomegat` and the displacement by `S_2` be `Y_2 = acos(omegat +phi)` 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 = 4a^2 cos^2phi/2` Hence, establish the conditions for constructive and destructive interference.(ii) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slit is increased;

Question

(i) 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 = acosomegat`
and the displacement by `S_2` be `Y_2 = acos(omegat +phi)` 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 = 4a^2 cos^2phi/2` Hence, establish the conditions for constructive and destructive interference.
(ii) What is the effect on the interference fringes in Young's double slit experiment when (i) the width of the source slit is increased; (ii) the monochromatic source is replaced by a source of white light?