Finding the angle at the apex of a rhomb with incoming linear wave

[happyparticle]

Homework Statement

Finding the angle at the apex (A) for which the outgoing beam is perpendicular to the side of a rhomb if the incoming plane wave is linearly polarized at 45 degrees to the plane of incidence and the beam is perpendicular to the first side.

Relevant Equations

$\theta_I = \theta_t = 0$

Hi,

Since I'm dealing with a rhombus, the angle at the bottom(A) and top(A) are the same. Thus, I only have to find the angle at the bottom since the incoming beam is already perpendicular to the side of the rhombus.

Since the incoming beam is perpendicular to the side $\theta_I = \theta_T = 0$ If I understood correctly.
And it seems to have no reflection.

I'm not sure if all those details are important to find the angle. However I can't put those pieces together.
It might be simple, but for some reasons I don't know how to begin.

Any help will be appreciate
Thanks

 

[haruspex]

Homework Statement:: Finding the angle at the apex (A) for which the outgoing beam is perpendicular to the side of a rhomb if the incoming plane wave is linearly polarized at 45 degrees to the plane of incidence and the beam is perpendicular to the first side.
Relevant Equations:: $\theta_I = \theta_t = 0$

Hi,

Since I'm dealing with a rhombus, the angle at the bottom(A) and top(A) are the same. Thus, I only have to find the angle at the bottom since the incoming beam is already perpendicular to the side of the rhombus.

Since the incoming beam is perpendicular to the side $\theta_I = \theta_T = 0$ If I understood correctly.
And it seems to have no reflection.

I'm not sure if all those details are important to find the angle. However I can't put those pieces together.
It might be simple, but for some reasons I don't know how to begin.
View attachment 299179

Any help will be appreciate
Thanks

I don’t understand the relevance of the polarisation, so I might not be the right person to assist.
But ignoring that, assign a variable to the angle A. What is the angle of incidence of the light at the first internal reflection?

 

[happyparticle]

What is the angle of incidence of the light at the first internal reflection?

The only thing I think off is 90-A = angle at the first reflection If it is want you mean.

 

[haruspex]

The only thing I think off is 90-A = angle at the first reflection If it is want you mean.

Ok, so what can you deduce about the angles of the obtuse triangle on the right?

 

[nasu]

Is the prism supposed to be bi-refringent? What is the context of this problem? Where did you get it from?

 

[happyparticle]

Is the prism supposed to be bi-refringent? What is the context of this problem? Where did you get it from?

I suppose it is bi-refringent, it is not mentioned. I wrote all that I have.

 

[nasu]

I don't see how the polarization is relevant either. Just do it by using the geometrical optics. @haruspex is already guiding you.

 

[happyparticle]

Ok, so what can you deduce about the angles of the obtuse triangle on the right?

We have $2 \theta_2 + \theta_1 = 180$
Is $\theta_2 = A$ where A is used ( 90-A = angle at the first reflection)

 

[haruspex]

We have $2 \theta_2 + \theta_1 = 180$
Is $\theta_2 = A$ where A is used ( 90-A = angle at the first reflection)

What do you know about the angles involved in a reflection?

 

[happyparticle]

Ah! $\theta_i = \theta_r$
Thus, the 2 angles from obtuse triangle are the same as the angle at the first reflection.

 

[haruspex]

Ah! $\theta_i = \theta_r$
Thus, the 2 angles from obtuse triangle are the same as the angle at the first reflection.

So what relationships do you have between all the angles now?
Post a diagram labelling all the angles so there's no confusion.

 

[happyparticle]

It seems good.

 

[haruspex]

View attachment 299220
It seems good.

Yes, though you do not explain how you arrived at that.