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August 2017 Can one make a laser out of cardboard?
Krzysztof Burdzy, Tvrtko Tadić
Ann. Appl. Probab. 27(4): 1951-1991 (August 2017). DOI: 10.1214/16-AAP1180


We consider two-dimensional and three-dimensional semi-infinite tubes made of “Lambertian” material, so that the distribution of the direction of a reflected light ray has the density proportional to the cosine of the angle with the normal vector. If the light source is far away from the opening of the tube then the exiting rays are (approximately) collimated in two dimensions but are not collimated in three dimensions. An observer looking into the three-dimensional tube will see “infinitely bright” spot at the center of vision. In other words, in three dimensions, the light brightness grows to infinity near the center as the light source moves away.


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Krzysztof Burdzy. Tvrtko Tadić. "Can one make a laser out of cardboard?." Ann. Appl. Probab. 27 (4) 1951 - 1991, August 2017.


Received: 1 July 2015; Revised: 1 January 2016; Published: August 2017
First available in Project Euclid: 30 August 2017

zbMATH: 1373.60080
MathSciNet: MR3693517
Digital Object Identifier: 10.1214/16-AAP1180

Primary: 37D50, 37H99, 60G50, 60K05

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.27 • No. 4 • August 2017
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