Calculating the angle of the transmitted electric field.

[Sniperuml]

Homework Statement

Plane polarized light is incident in air at an angle of incidence of 30 degrees on a glass surface with its electric field vector vibrating at 60 degrees to the plane of incidence. Calculate the angle between the transmitted electric field vector and the plane of incidence.

Homework Equations

n_i sin(theta_i) = n_tsin(theta_t)
n = 1.51 for glass

t_p = ((2n_i*cos(theta_i))/[(n_tcos(theta_i) + (n_icos(theta_t))]

t_s = ((2n_i*cos(theta_i))/[(n_icos(theta_i + n_tcos(theta_t))]

The Attempt at a Solution

The answer supplied is theta_gamma = 59.6 degrees. (supplied by professor)

I know the right way to approach this is to set tan(gamma) = ratio of the perpendicular part of the E-field over the parallel part of the E-field in the material (i.e. the glass). Rewrite equation to in terms of t_s and t_p and tan(gamma) in the incident.

How to actually do this? I have no idea. I got this far and it took my an entire weekend to get this far. This a question on a test, I got the highest grade and I am the only undergrad in the class, and we all still failed. Any ideas?

The attached .pdf is my attempts at solving the problems.

 

[Jhero]

I would approach this problem by first reviewing the relevant equations and principles related to light reflection and refraction at an interface between two media with different refractive indices. The equation ni sin(thetai) = ntsin(thetat) is known as Snell's law and it describes the relationship between the incident angle (thetai), the refractive indices of the two media (ni and nt), and the angle of refraction (thetat). This equation can be applied to both the parallel (tp) and perpendicular (ts) components of the electric field vector.

Next, I would identify the known values in the problem, such as the angle of incidence (30 degrees), the refractive index of glass (1.51), and the angle of the electric field vector (60 degrees). From there, I would use the equations tp = ((2ni*cos(thetai))/[(ntcos(thetai) + (nicos(thetat))] and ts = ((2ni*cos(thetai))/[(nicos(thetai + ntcos(thetat))] to calculate the parallel and perpendicular components of the electric field vector in the glass. Then, I would use the equation tan(gamma) = (ts/tp) to find the angle between the transmitted electric field vector and the plane of incidence (gamma).

In this case, the angle between the transmitted electric field vector and the plane of incidence is 59.6 degrees, as given by the professor. It is important to remember that this is just one possible approach to solving this problem and there may be other methods that could also yield the correct answer. it is important to be open to different approaches and to always double check your calculations to ensure accuracy.