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1. Consider a y-polarized electromagnetic wave with vacuum wavelength 600nm that is propagating in glass and then incident on a glass-air interface; use n=1.4 for glass. Take the interface surface to be the y-z plane, and the plane of incidence to be the x-z plane. Consider 2 incident angles, 45, and 80 degrees. Take the amplitude of the incident field to be Eo.
Write complete expressions for the reflected and transmitted electric fields If there are any evanescent fields, determine the depth of penetration into air.
I've determined the E-field to be perpendicular to the plane of incidence so
r(perpendicular)= (E0r/E0i)= (nicos(thetai)-ntcos(thetat))/nicos(thetai)+ntcos(thetat)
then snells law nisin(thetai)=ntsin(thetat)
Then Possibly the O.P.L= INtegral from S to P n(s)ds
OPL/lamda0=s/lamda
t=OPL/c
where OPL is the Optical path length, n(s) is the index of refraction incident as a function of position.
Okay, so I began with attempting to solve for the reflected E-field. So I first used Case 1 where thetai= 45. I solved for theta t, and got 30.3 degrees. then solved for the reflected amplitude and got -o.5016 (obtained by plugging in values to the E0r equation. So I wrote the Reflectance to be the following
r(perpendicualar)= -0.5016/Eo. I don't think that's right at all due to the fact that it should also refract in glass, then reflect so off air, and refract in air, I only took the case where it relfects of glass. I am almost completley stuck, tried reviewing sections to try and understand this problem better but haven't been able to. Could anyone just help shoot me in the right direction please? Thanks.
Write complete expressions for the reflected and transmitted electric fields If there are any evanescent fields, determine the depth of penetration into air.
Homework Equations
I've determined the E-field to be perpendicular to the plane of incidence so
r(perpendicular)= (E0r/E0i)= (nicos(thetai)-ntcos(thetat))/nicos(thetai)+ntcos(thetat)
then snells law nisin(thetai)=ntsin(thetat)
Then Possibly the O.P.L= INtegral from S to P n(s)ds
OPL/lamda0=s/lamda
t=OPL/c
where OPL is the Optical path length, n(s) is the index of refraction incident as a function of position.
The Attempt at a Solution
Okay, so I began with attempting to solve for the reflected E-field. So I first used Case 1 where thetai= 45. I solved for theta t, and got 30.3 degrees. then solved for the reflected amplitude and got -o.5016 (obtained by plugging in values to the E0r equation. So I wrote the Reflectance to be the following
r(perpendicualar)= -0.5016/Eo. I don't think that's right at all due to the fact that it should also refract in glass, then reflect so off air, and refract in air, I only took the case where it relfects of glass. I am almost completley stuck, tried reviewing sections to try and understand this problem better but haven't been able to. Could anyone just help shoot me in the right direction please? Thanks.