why doesn't the light from the headlights of your car cause an interference pattern?

It would if you had two lasers (monochromatic, inphase waves).

Light from headlight is not a single beam, it is millions of light beams combined into the same area.

The light from the headlights of a car does not cause an interference pattern because it is not a coherent source of light. In order for interference to occur, the light waves need to be coherent, which means that they have a constant phase relationship with each other.

Headlight beams are produced by multiple independent light sources within the headlights. Each individual source emits light with its own phase and directionality. As a result, the waves emitted from different sources do not have a consistent phase relationship and do not interfere with each other constructively or destructively to create an interference pattern.

Therefore, although the light from car headlights may appear to scatter or spread, it does not produce an interference pattern like the ones observed in experiments with coherent light sources, such as lasers.

The light emitted by the headlights of a car does not cause an interference pattern because it consists of incoherent light sources. In order to understand this, we need to delve into the concept of interference.

Interference is a phenomenon that occurs when two or more coherent light waves interact with each other. Coherent light waves have a constant phase relationship, meaning they maintain a fixed time difference between their peaks and troughs. When these coherent waves superimpose, they can either reinforce or cancel each other out, resulting in an interference pattern.

To produce an interference pattern, the light sources must be emitting a single wavelength of light, like those produced by lasers or certain types of filters. This coherence ensures that the individual light waves are in phase with one another, allowing them to create the alternating bright and dark fringes characteristic of an interference pattern.

However, the light emitted by car headlights is typically produced by incandescent bulbs or halogen lamps, which are sources of incoherent light. Incoherent light consists of various wavelengths that are not phase-related. Each light wave emitted by these sources has a different phase, preventing constructive or destructive interference from occurring.

Therefore, the light from car headlights does not form an interference pattern because the light waves are incoherent and do not maintain a consistent phase relationship.