(a) (i) Two independent mono chromatic sources of light cannot produced a sustained interference pattern'. Give reason.
(ii) Light waves each of amplitude ''a'' and frequency ''w'', emanating from two coherent light sources superpose at a point. If the displacements due to these waves is given by`y_(3)=a cos omega t and y_(2)=a cos(omega t+phi)` where `phi` is the phase difference between the two, obtain the expression for the resultant intensity at the point.
(b) In Young's double slit experiment, using monochromatic light of wavelength `lambda`, the intensity of light at a point on the screen where path difference is `lambda`, is K units. Find out the intensity of light at a point where path difference is `lambda//3`.

Explanation

The resultant displacement will be given by
`y=y_1+y_2`
`=a cos omega t + a cos (omega t+phi)`
`=a[cos omegat +acos (omegat+phi)]`
`=2acos (phi//12)cos (omegat+phi12)`
The amplitude of the resultant displacement is `2a cos (phi//12)`
The intensity of light is directly proportional to the square of amplitude of the wave. The resultant, intensity will be given by
`I=4a^2` or `a^2=I/4`