O-ray vs E-ray: Understanding Double Refraction

This article clarifies the difference between O-ray and E-ray, two phenomena observed in specific types of crystals.

The terms O-ray and E-ray stand for Ordinary ray and Extraordinary ray, respectively. These rays are associated with a special optical property called double refraction or birefringence. This effect is seen in anisotropic crystals like calcite, quartz, KDP, and rutile.

What is Double Refraction

When a single beam of unpolarized light strikes an anisotropic crystal (like calcite), the light splits into two beams at the crystal surface. These beams are the O-ray and the E-ray, as illustrated in Figure 1.

The key characteristic is that both O-ray and E-ray travel in different directions and at different speeds within the crystal. Furthermore, their planes of polarization are mutually orthogonal.

O-Ray | Ordinary Ray

• As depicted in the figure above, the plane of polarization of the O-ray is perpendicular to the plane of the image.
• It’s referred to as the ordinary ray because it behaves in a “normal” way.
• Crucially, the O-ray follows Snell’s law of refraction.
• The velocity of the O-ray (vo) is calculated as c/no, where ‘c’ is the speed of light and ‘no’ is the refractive index for the ordinary ray.

E-Ray | Extraordinary Ray

• In contrast to the O-ray, the plane of polarization of the E-ray lies within the same plane as the image in the figure.
• It’s called the extraordinary ray due to its unusual behavior.
• A key difference is that the E-ray does not follow Snell’s law of refraction.
• The velocity of the E-ray (ve) is calculated as c/ne, where ‘c’ is the speed of light and ‘ne’ is the refractive index for the extraordinary ray.

Important Note:

The velocities of the O-ray and E-ray are different in all directions except along one particular direction known as the optic axis. Along this optic axis, both the O-ray and E-ray travel at the same speed.

The effective refractive indices, no and ne, are known as the principal refractive indices of the crystal.

Conclusion

The key difference between the Ordinary ray (O-ray) and the Extraordinary ray (E-ray) lies in their propagation behavior within an anisotropic medium, such as a birefringent crystal. The O-ray follows Snell’s law and maintains a constant refractive index regardless of direction, while the E-ray experiences a variable refractive index depending on the propagation angle relative to the optical axis. This distinction leads to unique optical properties, including double refraction (birefringence), which is widely used in polarization optics, optical modulators and waveplates. Understanding these differences is essential for applications involving polarized light manipulation and optical communication technologies.