# Calculate the desired incident polarization of a light beam

• Corwin_S
In summary, the author is trying to find the polarization of an incoming beam of light that is linearly polarized (i.e., 45 degrees). They use Fresnel equations to determine the reflection coefficients of the s and p polarized components. They then use Snell's law to determine the angle of incidence. Finally, they use the reflection coefficients to find the polarization of the input.
Corwin_S
Hi I want to calculate the necessary incident polarization of a light beam at a given angle of incidence (theta_i) that reflects off BK7 glass (n = 1.5168) and is linearly polarized (i.e., 45 degrees). I know how to do similar calculations for incident natural unpolarized light, but not in the case of incoming polarized light.

Cheers

Corwin_S said:
Hi I want to calculate the necessary incident polarization of a light beam
What type of polarization is it, linear?

The reflected beam comes out linearly polarized (50/50 s/p). I'm trying to find the incoming beam's polarization (assume it is not circularly or ellipitically polarized).

Forget my previous comment, if the reflected light is linearly polarized then so is the incoming one for the case of external reflection (##n_2 > n_1##).
Anyway, you have Fresnel equations for TE and TM components:
$$\frac{E_r^{TE}}{E_i^{TE}} = \frac{n_1\cos \theta_1 - n_2\cos \theta_2}{n_1\cos \theta_1 + n_2\cos \theta_2}$$
$$\frac{E_r^{TM}}{E_i^{TM}} = \frac{n_2\cos \theta_1 - n_1\cos \theta_2}{n_2\cos \theta_1 + n_1\cos \theta_2}$$
Now it's required that ##E_r^{TE}=E_r^{TM}## and that ##\theta_1## is given, from which ##\theta_2## will follow from Snell's law. So, isn't it straightforward to get the ratio of the components of the incoming light?

This is completely correct. Those can be called the reflection coefficients of the s and p polarized components. I believe the correct way of determining the polarization of the input is to find the degree of polarization:

V = Ip/(Ip+In)
And I believe, although am not sure, that Ip = Rs + Rp and In = 1/2(Rp + Rn).

Hence given the specs n = 1.5154 @ 650 nm, and the incidence/reflectance angle = 50 degrees, I compute the degree of polarization to be ~66.67%.

I don't know if this is right though.

Corwin_S said:
This is completely correct. Those can be called the reflection coefficients of the s and p polarized components. I believe the correct way of determining the polarization of the input is to find the degree of polarization:

V = Ip/(Ip+In)
And I believe, although am not sure, that Ip = Rs + Rp and In = 1/2(Rp + Rn).

Hence given the specs n = 1.5154 @ 650 nm, and the incidence/reflectance angle = 50 degrees, I compute the degree of polarization to be ~66.67%.

I don't know if this is right though.
Correction, n =1.5145

## What is the desired incident polarization of a light beam?

The desired incident polarization of a light beam refers to the specific orientation of the electric field of the light wave as it enters a material or interacts with an object. This can be either linear, circular, or elliptical polarization, and is determined by the direction and amplitude of the electric field vector.

## Why is it important to calculate the desired incident polarization of a light beam?

Calculating the desired incident polarization of a light beam is important because it allows us to understand and control how the light will interact with different materials and objects. This can affect the properties of the light itself, as well as the properties of the material or object it is interacting with.

## What factors affect the desired incident polarization of a light beam?

The desired incident polarization of a light beam can be affected by several factors, including the angle of incidence, the refractive index of the material, and the presence of any birefringent materials in the path of the light beam. Additionally, the polarization of the light may change if it reflects off of a surface or passes through a polarizing filter.

## How is the desired incident polarization of a light beam calculated?

The desired incident polarization of a light beam can be calculated using mathematical equations that take into account the properties of the light wave, the material it is interacting with, and any other relevant factors. These calculations may involve vector algebra and trigonometry, and can be done using specialized software or programming languages.

## Can the desired incident polarization of a light beam be manipulated?

Yes, the desired incident polarization of a light beam can be manipulated using various techniques such as polarizing filters, wave plates, and birefringent materials. These methods allow us to control the orientation and intensity of the electric field of the light wave, and therefore change its desired incident polarization.

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