# Snell's Law in birefringent materials

• bayners123
In summary, when considering the behavior of light at a boundary between two birefringent materials with perpendicular optical axes, Snell's equation can be used to determine the angle of refraction. For linearly polarized light, the refractive indices of the two materials are different. For light polarized in the plane of reflection, the choice of refractive index depends on the direction of the light's oscillation. When considering different types of polarization (planar, perpendicular, circular, and unpolarized), the refractive index chosen for the incident light may vary.
bayners123

## Homework Statement

I'm trying to work out what happens why light hits a boundary between two birefringent materials with their optical axis perpendicular. It's hard to describe so I've attached a diagram. The upper wedge has an optical axis pointing upwards, the lower wedge has it coming out of the page.

Snell's equation is $$sin(\theta_T) = \frac{n_1}{n_2} sin(\theta_i)$$
For linearly polarized light out of the plane of reflection (s polarization) $$n_1 = n_o$$ and $$n_2 = n_e$$ (both slabs are made of the same material with different orientations).
For light polarized in the plane though I'm confused: as it comes in the light oscillates in the optical axis but once it is reflected it oscillates perpendicular to it. What should I take for n1?

Also, the question asks for ray diagrams in the case of a) planar polarization b) perpendicular polarization c) circular polarization and d) unpolarized light. I've discussed a) and b), but am I right in thinking that c) and d) are just both rays happening at once with half the intensity?

## Homework Equations

$$sin(\theta_T) = \frac{n_1}{n_2} sin(\theta_i)$$

## The Attempt at a Solution

#### Attachments

• photo.JPG
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For planar polarization, I believe n_1 is just the ordinary refractive index, since the light oscillates parallel to the optical axis. For perpendicular polarization, I think n_1 should be the extraordinary refractive index, since the light oscillates in the opposite direction. For circular polarization, I think it is just both rays happening at once with half the intensity. For unpolarized light, I think it is the same as circular polarization, but with equal intensities for each ray.

## 1. What is Snell's Law?

Snell's Law is a fundamental principle in optics that describes the relationship between the angles of incidence and refraction of light at the interface between two different materials. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two materials.

## 2. What are birefringent materials?

Birefringent materials are substances that have two different refractive indices, depending on the polarization of the incident light. This means that the speed of light is different in different directions within the material, resulting in the splitting of light into two perpendicular rays.

## 3. How does birefringence affect Snell's Law?

In birefringent materials, Snell's Law still holds true, but the refractive indices used in the calculation are different for the two polarizations of light. This means that the angle of refraction will also be different for the two polarizations, resulting in a phenomenon known as double refraction.

## 4. What is the significance of Snell's Law in birefringent materials?

Snell's Law is important in birefringent materials because it allows us to predict the direction of light as it passes through the material. This is crucial in applications such as polarizing filters and liquid crystal displays, where controlling the polarization of light is necessary.

## 5. Are there any real-world applications of Snell's Law in birefringent materials?

Yes, there are many applications of Snell's Law in birefringent materials. Some examples include polarizing sunglasses, liquid crystal displays, polarizing filters in cameras, and waveplates used in optical communication systems. Snell's Law is also used in the study of crystallography to determine the orientation of crystals.

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