(a) In Young's double slit experiment, the two slits are illuminated by two different lamps having same wavelength of light. Explain with reason, whether interference pattern will be observed on the screen or not.
(b) Light waves waves from two coherent sources arrive at two points on a screen with path differences of 0 and `lamda//2`. Find the ratio of intensities at the points.

Explanation

(a) Condition for sustainable interference is that both the sources must be coherent. (Same wavelength, and same or constant phase difference). Two sources are monochromatic if they have same frequency and wavelength. Since the sources are independent, they have different phase with irregular differences, so, they are not coherent.
(b) As the path difference is 0, so from, `varphi = (2pi)/(lamda) Deltax, varphi= 0`
and for `.^(lamda)//_(2)` path diffrence `varphi = (sqrt2pi)/(sqrtlamda) xx (sqrt(lamda))/(sqrt2) = pi`
So `I = 4I_(0) "cos"^(2) (varphi)/(2) = 4I_(0) cos^(2) 0 = 4I_(0)`...(i)
and `.^(I_(lamda))//_(2) = 4I_(0) "cos"^(2) (pi)/(2) = 4I_(0) xx 0 = 0` ...(ii)
Ratio is `.^(I_(0))//_(I_(lamda//2)) = (4I_(0))/(0) = oo`