TY - JOUR
T1 - The refraction and reflection laws from a complete integral of the eikonal equation and Huygens' principle
AU - Castro-Ramos, Jorge
AU - Juárez-Reyes, Salvador Alejandro
AU - Marcelino-Aranda, Mariana
AU - Ortega-Vidals, Paula
AU - Silva-Ortigoza, Gilberto
AU - Silva-Ortigoza, Ramón
AU - Suárez-Xique, Román
N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - In this work we assume that we have two given optical media with constant refraction indexes, which are separated by an arbitrary refracting surface. In one of the optical media we place a point light source at an arbitrary position. The aim of this work is to use a particular complete integral of the eikonal equation and Huygens' principle to obtain the refraction and reflection laws. We remark that this complete integral associates a new point light source with each light ray that arrives at the refracting surface. This means that by using only this complete integral it is not possible to determine the direction of propagation of the refracted light rays; the direction of propagation is obtained by imposing two extra conditions on the complete integral which are equivalent to Huygens' principle (in two dimensions, only one condition is needed). Finally, we establish the connection between the complete integral used here and that derived by using the k-function procedure introduced by Stavroudis, which works with plane wavefronts instead of spherical ones.
AB - In this work we assume that we have two given optical media with constant refraction indexes, which are separated by an arbitrary refracting surface. In one of the optical media we place a point light source at an arbitrary position. The aim of this work is to use a particular complete integral of the eikonal equation and Huygens' principle to obtain the refraction and reflection laws. We remark that this complete integral associates a new point light source with each light ray that arrives at the refracting surface. This means that by using only this complete integral it is not possible to determine the direction of propagation of the refracted light rays; the direction of propagation is obtained by imposing two extra conditions on the complete integral which are equivalent to Huygens' principle (in two dimensions, only one condition is needed). Finally, we establish the connection between the complete integral used here and that derived by using the k-function procedure introduced by Stavroudis, which works with plane wavefronts instead of spherical ones.
KW - Geometric optics
KW - Reflection
KW - Refraction
UR - http://www.scopus.com/inward/record.url?scp=84918523042&partnerID=8YFLogxK
U2 - 10.1088/2040-8978/17/1/015601
DO - 10.1088/2040-8978/17/1/015601
M3 - Artículo
SN - 2040-8978
VL - 17
JO - Journal of Optics (United Kingdom)
JF - Journal of Optics (United Kingdom)
IS - 1
M1 - 015601
ER -