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Black Body Radiation and the Photon Gas
Published in Jeffrey Olafsen, Sturge’s Statistical and Thermal Physics, 2019
Astronomical magnitude is a negative logarithmic scale of luminosity, in which an increase of one magnitude represents a decrease in luminosity by a factor of 2.5 (approximately e). Thus, a star of apparent magnitude 5 is a factor (2.5)5≈100 more luminous (that is, it appears to be a factor ∼100 brighter) than a star of magnitude 10. If star A has an apparent magnitude equal to star B when viewed through a yellow filter (mean wavelength 550 nm) and has one higher apparent magnitude when viewed through a blue filter (mean wavelength 440 nm), what is the surface temperature of star A, if that of star B is known to be 6000 K? Assume that both stars are black bodies, that Wien’s law applies in this spectral region, and that the bandpass of each filter (that is, the spread of wavelength transmitted) is the same, and is small enough that the spectral density can be taken to be that at the mean wavelength23
Astronomical Telescopes
Published in Daniel Malacara-Hernández, Zacarías Malacara-Hernández, Handbook of OPTICAL DESIGN, 2017
Daniel Malacara-Hernández, Zacarías Malacara-Hernández
The magnitude of a star is an indication of its brightness. The greater the magnitude, the fainter the star. The magnitude of a star is an arbitrary scale invented by the Greeks. According to them, the brightest stars in the sky had magnitude 1 and the faintest had magnitude 6. The same basic definition is now used, but with a more formal and mathematical meaning. Now we know that, according to the psychophysical law of Fetchner, the optical sensation in the eye is directly proportional to the logarithm of the luminous excitation. On the basis of this effect, John Herschel in 1830 defined that the first-magnitude star is 100 times brighter than the sixth-magnitude star. Thus, the brightness of a star one magnitude higher is (100)1/5 = 2.512 times larger.
Photometry
Published in C. R. Kitchin, Astrophysical Techniques, 2020
The faintest stars visible to the naked eye, from the definition of the scale, are of magnitude six; this is termed the ‘limiting magnitude of the eye’. For point sources, the brightness is increased by the use of a telescope by a factor, G, which is called the ‘light grasp of the telescope’ (Section 1.1). Because the dark-adapted human eye has a pupil diameter of about 7 mm, G is given by () G≈ 2×104d2
On Illumination Vector Quantities Due to Area Light Sources: Comparison of Two Calculation Approaches
Published in LEUKOS, 2022
Rizki A. Mangkuto, Mochamad Donny Koerniawan
In scenes with a single point source, the vector illuminance magnitude |E| would be equal to the Emax. In scenes with an area source, however, the ΔEmax due to each element cannot be summed directly. Instead, the ΔEmax,i shall first be projected onto the x-, y-, and z-axes, based on the corresponding zenith angle γi and azimuth angle ψi (Fig. 1), to yield the contribution of cubic illuminances at x+, x–, y+, y–, z+, and z – directions as follows:
The use of acoustic streaming in Sub-micron particle sorting
Published in Aerosol Science and Technology, 2022
Tsz Wai Lai, Sau Chung Fu, Ka Chung Chan, Christopher Y. H. Chao
The geometry of the microchannel has altered the acoustic streaming velocity and pattern accordingly. In Figure 6, the arrows show the direction of the streaming flow. The size of the arrows represents the magnitude of the streaming velocity in the logarithmic scale. In all cases, the streaming pattern is also left-right symmetric. Four vortices are generated in the bulk, two above the pressure node line and two below, which are counter-rotating compared to the neighboring vortices. They are Rayleigh’s streaming. Due to the different length-scale, Schlichting streaming cannot be shown in Figure 6. The region of Schlichting streaming is very narrow near the walls. In Figure 6, the highest streaming velocity is found near the sidewalls. It may be explained by the fact that Rayleigh’s streaming is induced by the strong streaming vortices formed inside the viscous layer (Schlichting streaming), and the streaming velocity is the largest at the point where the streaming flow is initiated. The flow becomes weaker as it moves away from the sidewalls.
Entanglement-enabled interferometry using telescopic arrays
Published in Journal of Modern Optics, 2020
Siddhartha Santra, Brian T. Kirby, Vladimir S. Malinovsky, Michael Brodsky
With telescopes of larger aperture the flux of photons is higher. This would require correspondingly higher entanglement generation rates to utilize the larger number of photons received per unit time. With currently available technology the quantum-enhanced interferometric scheme is best suited for measurements of weak astronomical sources if large aperture telescopes are available. For example, if telescopes with diameter 1 m are used then sources with 100 times lesser photon flux on earth than Vega would require the same entanglement generation rate of . In terms of the apparent magnitude system used in astronomy (apparent magnitude of an object in astronomy is defined as where is the flux of photons from the object on earth in the spectral band around x and is the flux on earth from Vega in the same band. Thus weaker sources have a higher apparent magnitude), currently the quantum-enhanced scheme is best suited for the study of weak sources of apparent magnitude 5 or higher for telescopes of diameter 1 m.