"If you illuminate two pinholes using two lamps, the interference pattern will not be observed" - Explain.

(N/A) To observe a stable interference pattern, the two sources of light must be coherent, meaning they must maintain a constant phase difference over time.
When two independent light sources (like two sodium lamps) are used to illuminate two pinholes $S_1$ and $S_2$, the light waves emitted by each lamp undergo abrupt and random phase changes in very short time intervals (on the order of $10^{-9} \text{ s}$).
Because these phase changes are independent and random for each lamp, there is no fixed phase relationship between the light waves emerging from $S_1$ and $S_2$. Consequently, the sources are incoherent.
In the case of incoherent sources, the intensities of the light waves add up rather than interfering constructively and destructively to form a pattern. Therefore, the screen will show a uniform illumination instead of distinct bright and dark interference fringes.