A cardboard box can catch fire if exposed to an intense heat source, including direct sunlight for an extended period. However, the Sun's rays alone, even if they are always shining on a cardboard box, are typically not sufficient to ignite it under normal circumstances.
Cardboard is a flammable material composed of cellulose fibers derived from wood. To ignite, it requires a heat source that raises its temperature beyond its ignition point, which is around 450 degrees Fahrenheit (232 degrees Celsius) for typical cardboard. While the Sun's rays can generate heat, the ambient temperature and the cardboard's exposure to direct sunlight are usually not enough to reach that ignition point.
That said, there are scenarios where a cardboard box exposed to continuous sunlight might be at an increased risk of catching fire. For example, if the cardboard is placed in a way that focuses the Sun's rays to a concentrated spot, such as using a magnifying glass or if reflective surfaces are present, it could potentially lead to a localized heating effect that may ignite the cardboard. This is similar to the concept of using a magnifying glass to start a fire by concentrating sunlight onto a specific point.
In normal conditions, however, a cardboard box exposed to the Sun's rays alone will not spontaneously catch fire.