I have been racking my mind over the double slit experiment. There are many excellent demonstrations of the double slit experiment, some with water, and some with light, available online. I am familiar with expressing a wave as:
and vartiants, so I have no problem envisioning and interference pattern. However, the analogy (if it is one) of light and water interference seems to break down to me because two sources of waves in the water can clearly create a diffraction patter with no slits. Two sources of light do not, in general,do the same thing, because I can turn on a few of my lamps and not get a diffraction pattern!
I know that the light sources are out of phase $\Delta\phi_0$, but could someone be so kind as to explain to me as to why they become in phase while passing through the slits?
Thank you kindly. (I have not seen two out of phase wave sources in water being made to pass through two slits.)