Final answer:
Headlights may dim due to temporary voltage drops when additional current is demanded from a car battery. Gradual dimming of headlights occurs as the battery depletes.
Step-by-step explanation:
The observation about headlights dimming when additional power loads are placed on a car's battery is related to the electrical properties of the battery itself. When the refrigerator motor starts or a car engine is ignited while the interior lights are on, these lights may dim momentarily due to a temporary voltage drop in the circuit. This happens because the battery is suddenly required to supply more current to the additional load, causing an internal voltage drop due to its internal resistance. Similarly, this is why car headlights dim gradually as the battery runs down; the battery's output voltage decreases as the available charge is depleted, rather than the lights simply blinking off immediately when the battery is empty.
To answer the specific problem involving the running lights being left on - the driver calculates how long the car's headlights will last based on the battery's capacity and the power consumption of the headlights. Knowing the battery's rating is 100 Ah, and given that each 12-V headlight is rated at 40 W, the driver could use these figures to estimate the duration the headlights can run.
The ability to resolve two headlights as separate points of light depends on the resolving power of the human eye, which in turn depends on the pupil diameter and the wavelength of light. The driver might be interested in the maximum distance at which the headlights can be resolved as distinct points – this calculation involves the ray optics and properties of human vision.