Wien approximation

Abstract: Introductory physics and astronomy courses commonly use Wien’s displacement law to explain the colors of blackbodies, including the Sun and other stars, in terms of their temperatures. We argue here that focusing on the peak of the blackbody spectrum is misleading for three reasons. First, the Planck curve is too broad for an individual spectral color to stand out. Second, the location of the peak of the Planck curve depends on the choice of the independent variable in the plot. And third, Wien’s displacement law is seldom used in actual practice to find a temperature and direct fitting to the Planck function is preferable. We discuss these flaws and argue that, at the introductory level, presentation of blackbody radiation in terms of photon statistics would be more effective pedagogically. The average energy of the emitted photons would then be presented in place of Wien’s displacement law, and discussion of the Stefan-Boltzmann law would include the total number of photons emitted per second. Finally, we suggest that the Planck spectrum is most appropriately plotted as a “spectral energy density per fractional bandwidth distribution,” using a logarithmic scale for the wavelength or frequency.

Abstract: We have analyzed high-resolution, digital, photometric images of solar active regions made at various center-limb positions on 21–24 July, 1983. The images were made at three continuum wavelengths: 5245 A in the green (bandpass 1.5 A), 6264 A in the red (bandpass 1.5 A), 10 000 A in the infrared (bandpass 3 A), and also at 8662 A in the Caii infrared line (bandpass 3 A). In all continuum colors, the contrasts of facular patches, as opposed to individual facular elements, appear to behave as linear functions of 1/cos θ, where θ is the heliocentric angle (μ = 0 at the limb, 1 at disk center). The relative contrasts in the different continuum colors are roughly proportional to (wavelength)-1, as expected from a Planck distributioin in the Wien approximation. The observed variation of the relative contrasts with center-limb position is compared to two simple theoretical models.

Abstract: A Taylor expansion can be used to linearize the Planck function that governs the emission from a material at a given temperature. Such a linearization is more accurate than using Wien's approximation. This approach can be used to improve the accuracy of those logarithms that currently utilize Wien's approximation, such as the alpha residual and alpha emissivity techniques.

Abstract: I T IS well known that Wien’s displacement law takes a different formwhenPlanck’s lawisexpressedintermsoffrequencythanthat in terms of wavelength (in vacuum) [1,2]. This can be explained by the different functional relationships because the wavelength is inversely proportional to the frequency of electromagnetic radiation. By introducing a logarithmic frequencyorwavelength scale, aunified Wien’s displacement law is obtained regardless of whether the frequency or wavelength is used as the independent variable. The new characteristic wavelength is approximately 26.6% longer than the conventional Wien’s displacement law in terms of wavelength.