Co-authors: Pharaoh John and Mee "not I" Zatarain
Abstract: We will categorize various paths as optically thin or thick. An optically thin path allows photons to transmit through, while an optically thick path absorbs and scatters photons.
The longer the pathlength of a photon through a scattering or absorbing media, the higher chance it will be scattered or absorbed.
a. The path from the center of the sun to us is optically thick since most of the photons will be scattered before they exit the sun. We cannot see the center of the sun since after traveling a certain depth into the sun's surface the sun becomes optically thick.
b. The path from the center of the sun to us for neutrinos is 'thin'. We based this off the fact that neutrinos were once a candidate for dark matter, and thus they qualify as dark, or non-interacting, and would not be scattered or absorbed as they traveled out of the sun.
c. Earth's atmosphere near peak frequency of CMB is optically thin since ground-based telescopes have been used to measure CMB homogeneity, so CMB radio-waves must penetrate earth's atmosphere. Also, we can hear satellite based XM radio-waves like Sirius, confirming earth's atmosphere is 'optically' thin to radio waves.
d. Earth's atmosphere is predominantly nitrogen and oxygen. Photons with energy of 13.7 eV (ionization energy of H) correspond to the first energy transition of an electron in hydrogen. Photons that hit hydrogen will excite the electron to the second energy level, the electron will jump down to the first level and reemit the photon. Hence hydrogen will scatter electrons at 13.7 eV. However, very little of the Earth's atmosphere is hydrogen so photons will pass through the atmosphere, which is correspondingly optically thin.
e. Cloudy days are generally darker, so clouds are optically thick. Clouds are mostly water vapor which scatters photons. Clouds from an above-earth view are white since the tops scatter, and dark from ground perspective since photons don't pass through.
f. Earth's atmosphere is optically thin for near-UV sunburn causing photons at the beach since we've all been sunburned on cloudy days in southern California.
g. Our clothes are optically thin for soft X-rays at airport scanners seeing as all the TSA officials in LAX have had the wonderful opportunity of seeing me naked.
h. Our bodies are mostly optically thick since soft X-rays at scanners don't penetrate through bone. However, we get a colored read-out with some hint of skeletal structure.
i. Our flesh is optically thin for medical X-rays since their purpose is to study bone structure, and we have endoskeletons.
j. Our bones are optically thick for medical X-rays. They are meant to study bone structure not to penetrate through them.
k. Random unidentified astrophysical objects with frequency distribution of blackbodies are optically thick since blackbodies are perfect emitters. Photons hitting them will not pass through but will be scattered.
Optically thin media:
Optically thick media:
I like the pictures, especially the "optically thick media" :)
ReplyDeleteYou made a good point on Earth's atmosphere for 13.7 eV. Earth's atmosphere is actually optically thick in the UV, and I thought it was because of hydrogen, but it turns out that it's because of oxygen! Who knew. However, hydrogen is an important absorber in the space between stars. Because the hydrogen gas in the clouds in which stars are born, the UV emission from young stars gets absorbed by hydrogen gas close to the stars, so that we don't actually see their UV emission.