The relationship between light and heat is that light can carry energy, and when light is absorbed by an object, it can be converted into heat. When light interacts with matter, the energy of the light can cause the atoms or molecules in the material to vibrate, which results in an increase in the overall thermal energy of the object. This increase in thermal energy is perceived as heat.
Regarding the wavelength of light, light is an electromagnetic wave, and all electromagnetic waves, including light, have a wavelength. The wavelength of light determines its color or frequency. Different objects can emit light at different wavelengths depending on their temperature and composition. For example, an object that is heated to a high temperature, like a glowing piece of metal, emits light at shorter wavelengths, typically in the visible range, which our eyes perceive as light. On the other hand, cooler objects, such as a warm cup of coffee or a human body, emit light at longer wavelengths, typically in the infrared range, which we cannot see but can feel as heat.
In summary, light always has a wavelength, and the wavelength of light can vary depending on the object emitting the light and its temperature. The relationship between light and heat is that light can transfer energy to matter, causing an increase in the thermal energy of the object and generating heat.