Plane wave angle of incidence calculation

[quantumguy45]

Good afternoon! Please help me figure out the mathematics of this simple plane wave question!

1. Homework Statement

2. Homework Equations
n1*sin(theta1)=n2*sin(theta2)

The Attempt at a Solution

I need help calculating the angle of incidence.
I found the propagation vector for incidence: ki=2*pi / lambda0 = 4 um
n1= 1 since we are given lambda0
I have n2 = 1.5
I know Snell's law is n1*sin(theta1)=n2*sin(theta2)
What vital information am I missing to solve this? I feel like its staring me in the face yet I'm unable to grasp it.

Thanks so much!

 

[Charles Link]

I'm assuming it is a transverse electromagnetic wave with some kind of linear polarization. I'm puzzled as to how the transmitted wave could have its magnetic field pointing only in the y direction perpendicular to the interface. That should mean that the transmitted wave must be propagating parallel to the interface. I'm stuck. Perhaps someone else can give an input. It doesn't look like a simple problem. I question whether the problem may have been misstated, but I could be missing something.

 

[quantumguy45]

I'm assuming it is a transverse electromagnetic wave with some kind of linear polarization. I'm puzzled as to how the transmitted wave could have its magnetic field pointing only in the y direction perpendicular to the interface. That should mean that the transmitted wave must be propagating parallel to the interface. I'm stuck. Perhaps someone else can give an input. It doesn't look like a simple problem. I question whether the problem may have been misstated, but I could be missing something.

I have a question, since I found k_i= 4um, can I just say the propagation vector for the incident wave is (4y+4z) therefore the angle of incidence would be arctan(4/4) = 45 degrees? Using this then:
1*sin 45=1.5 sin*(theta_t)
theta_t= 28 degrees?

 

[Charles Link]

I have a question, since I found k_i= 4um, can I just say the propagation vector for the incident wave is (4y+4z) therefore the angle of incidence would be arctan(4/4) = 45 degrees? Using this then:
1*sin 45=1.5 sin*(theta_t)
theta_t= 28 degrees?

I don't see a solution. Usually the z direction is taken as perpendicular to the interface in optics problems. Perhaps it is a typo, or perhaps I am missing the obvious, but I don't see a solution. @vanhees71 Could you take a look at this please. Am I missing something? I believe it is a flawed problem, but perhaps you can see a solution.

 

[quantumguy45]

Can I use tanΘi= n2/n1? I'm probably more lost than you are so I'm just looking for a spark to figure this out!

 

[Charles Link]

Can I use tanΘi= n2/n1? I'm probably more lost than you are so I'm just looking for a spark to figure this out!

See my edited post above. I've requested another fellow who has considerable expertise to take a look at it. I'm stuck.

 

[Charles Link]

Just an additional note: Usually problems like this specify the incident and/or transmitted ## \vec{k} ## vector, and they might ask you to solve for the reflected ## \vec{k} ##. They take a little bit of work, but they are interesting problems in vector algebra.