When two lamps are placed side by side so that light from both bulbs combine, no interference effects are observed because the light waves from one lamp are emitted independently of those of the other lamp.

Light waves from such sources of light (also called incoherent sources) undergo random phase changes in time intervals less than a nanosecond, and the conditions for any kind of interference are maintained only for such small time intervals, which the ordinary eye cannot perceive.

To understand why intensities add linearly, see this answer written by @Farcher:

Net intensity for interference from incoherent sources

Hope this helps.

When two lamps are placed side by side so that light from both lamps combine, no interference effects are observed because the light waves from one lamp are emitted independently of those of the other lamp.

Light waves from such sources of light (also called incoherent sources) undergo random phase changes in time intervals less than a nanosecond, and the conditions for any kind of interference are maintained only for such small time intervals, which the ordinary eye cannot perceive.

To understand why intensities add linearly, see this answer written by @Farcher:

Net intensity for interference from incoherent sources

Hope this helps.