TY - JOUR
T1 - Exact mirror equation via Berry's caustic touching theorem
T2 - plane and spherical mirrors
AU - Silva-Ortigoza, Gilberto
AU - Julian-Macias, Israel
AU - Gonzalez-Juarez, Adriana
AU - Espindola-Ramos, Ernesto
AU - Silva-Ortigoza, Ramon
AU - Marciano-Melchor, Magdalena
N1 - Publisher Copyright:
© 2022 Optica Publishing Group.
PY - 2022/4
Y1 - 2022/4
N2 - In this work, we assume that in free space we have an observer, a smooth mirror, and an object placed at arbitrary positions. The aim is to obtain, within the geometrical optics approximation, an exact set of equations that gives the image position of the object registered by the observer. The general results are applied to plane and spherical mirrors, as an application of the caustic touching theorem introduced by Berry; the regions where the observer can receive zero, one, two, three, and one circle of reflected light rays are determined. Furthermore, we show that under the restricted paraxial approximation, that is, when sin ψ≈ ψ and cos ψ≈1, the exact set of equations provides thewell-knownmirror equation.
AB - In this work, we assume that in free space we have an observer, a smooth mirror, and an object placed at arbitrary positions. The aim is to obtain, within the geometrical optics approximation, an exact set of equations that gives the image position of the object registered by the observer. The general results are applied to plane and spherical mirrors, as an application of the caustic touching theorem introduced by Berry; the regions where the observer can receive zero, one, two, three, and one circle of reflected light rays are determined. Furthermore, we show that under the restricted paraxial approximation, that is, when sin ψ≈ ψ and cos ψ≈1, the exact set of equations provides thewell-knownmirror equation.
UR - http://www.scopus.com/inward/record.url?scp=85127311670&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.452843
DO - 10.1364/JOSAA.452843
M3 - Artículo
C2 - 35471399
AN - SCOPUS:85127311670
SN - 1084-7529
VL - 39
SP - 726
EP - 735
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
IS - 4
ER -