The human skin is "selective" when it comes to the absorption of the solar radiation that strikes it perpendicularly. The skin absorbs only 50 percent of the incident radiation with wavelengths between \(\lambda_{1}=0.517 \mu \mathrm{m}\) and \(\lambda_{2}=1.552 \mu \mathrm{m}\). The radiation with wavelengths shorter than \(\lambda_{1}\) and longer than \(\lambda_{2}\) is fully absorbed. The solar surface may be modeled as a blackbody with effective surface temperature of \(5800 \mathrm{~K}\). Calculate the fraction of the incident solar radiation that is absorbed by the human skin.

Question: Calculate the fraction of the incident solar radiation absorbed by the human skin, given that the skin absorbs 100% of the radiation with wavelengths shorter than 0.517 µm and longer than 1.552 µm, and 50% of the radiation with wavelengths between 0.517 µm and 1.552 µm. The solar surface temperature is 5800 K. Solution: To find the fraction of the absorbed solar radiation, first calculate the energy emitted by the blackbody in the given wavelength range using Planck's radiation formula. Divide this range into three parts: wavelengths shorter than 0.517 µm, wavelengths between 0.517 µm and 1.552 µm, and wavelengths longer than 1.552 µm. Then, calculate the energy absorbed by the human skin by adding the energy absorbed in each wavelength range. Finally, divide the absorbed energy by the total energy emitted by the blackbody, and find the fraction of the absorbed energy.