The relationship between the wavelength of emitted light from a hot object and its temperature is described by a principle known as Wien's displacement law. According to Wien's law, the wavelength at which the maximum intensity of radiation occurs is inversely proportional to the temperature of the object.
Mathematically, Wien's displacement law is expressed as:
λ_max = b / T
where: λ_max is the wavelength at which the maximum intensity occurs, b is Wien's displacement constant (approximately equal to 2.898 × 10^(-3) meters per Kelvin), T is the temperature of the object in Kelvin.
This means that as the temperature of a hot object increases, the wavelength at which the maximum intensity of radiation occurs shifts to shorter wavelengths (towards the blue and ultraviolet region). In contrast, as the temperature decreases, the peak wavelength shifts to longer wavelengths (towards the red and infrared region).
This phenomenon can be observed in everyday life, for example, when heating a metal rod. Initially, it appears red (longer wavelengths) and becomes orange, yellow, and eventually bluish-white (shorter wavelengths) as it gets hotter.