Why does the visible spectrum of light lie between wavelengths 400 nm to 700 nm?

Ask any high school kid, “What is the visible spectrum of the electromagnetic (EM) radiation” and most will correctly answer that the visible spectrum is that part of the EM radiation which can be seen by human eyes and lies in the wavelength range between 300nm and 700nm. But few ever ponder on the question, why do human eyes see between 300 nm and 700 nm. To answer this question we need to understand the relation between the black-body radiation and temperature.

Every blackbody at a temperature above 0 kelvin (-273^oC) emits EM radiation. Rather than emitting radiation at a single wavelength, the blackbody emits a range or a spectrum. A curve can be constructed with λ on the x-axis and intensity of the radiation on the y-axis. This is called the black-body radiation curve. The curve is bell shaped with the intensity of radiation peaking at a certain λ, called λ_max. Wilhelm Wien discovered that the EM spectrum of black-body radiation shifts towards shorter wavelengths as the temperature increases. The equation describing this shift is written as:

λ_{max =} b/T

where, T is the temperature in kelvins and b is a constant called Wien’s displacement constant.

The effective temperature of the sun’s surface is 5778 K, which puts out peak radiation at about 500 nm. This is the green portion of the light, exactly the same as the peak intensity of the human eye.

From an evolutionary perspective it makes perfect sense for diurnal animals like humans to develop eyes that are most sensitive to that part of the spectrum which is most abundant. But not all animals need to sense the visible spectrum to survive. Snakes such as pit vipers prey on warm blooded mammals like rats which maintain their body temperatures at around 310 K, which is warmer than their surroundings. This temperature corresponds to a peak radiation at around 10 µm in the far infrared. They have therefore evolved infrared sensing organs for detecting these wavelengths to aid them in hunting.

In summary, human eyes are sensitive to the 400 nm – 700 nm spectrum of the EM radiation because this is the most abundant radiation on earth during day time. The temperature of the sun’s surface is the reason that the visible spectrum is the most abundant.