## Refractive Index (Index of Refraction)

Refractive Index (Index of Refraction) is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density. The refractive index variable is most commonly symbolized by the letter **n** or **n'** in descriptive text and mathematical equations.

As presented in the figure above, a wavefront incident upon a plane surface separating two media is refracted upon entering the second medium if the incident wave is oblique to the surface. The incident angle (**θ(1)**) is related to the refraction angle (**θ(2)**) by the simple relationship known as **Snell's law:**

Where **n** represents the refractive indices of material 1 and material 2 and **θ** are the angles of light traveling through these materials with respect to the normal. There are several important points that can be drawn from this equation. When **n(1)** is greater than **n(2)**, the angle of refraction is always larger than the angle of incidence. Alternatively when **n(2)** is greater than **n(1)** the angle of refraction is always smaller than the angle of incidence. When the two refractive indices are equal (**n(1)** = **n(2)**), then the light is passed through without refraction.

In optical microscopy, refractive index is an important variable in calculating numerical aperture, which is a measure of the light-gathering and resolving power of an objective. In most instances, the imaging medium for microscopy is air, but high-magnification objectives often employ oil or a similar liquid between the objective front lens and the specimen to improve resolution. The numerical aperture equation is given by**:**

where **n** is the refractive index of the imaging medium and **θ** is the angular aperture of the objective. It is obvious from the equation that increasing the refractive index by replacing the imaging medium from air (refractive index = 1.000) with a low-dispersion oil (refractive index = 1.515) dramatically increases the numerical aperture.

Snell's law was originally defined by the relationship between the incident angles and the ratio of the velocities of light in the two media. The **refractive index** or **index of refraction** is the ratio between the velocity of light (**c**) in free space (for all practical purposes, either air or a vacuum) and its velocity **η** in a particular medium**:**

As the refractive index of a material increases, the greater the extent to which a light beam is deflected (or refracted) upon entering or leaving the material. The refractive index of a medium is dependent (to some extent) upon the frequency of light passing through, with the highest frequencies having the highest values of **n**. For example, in ordinary glass the refractive index for violet light is about one percent greater than that for red light. A consequence of this phenomenon is that each wavelength experiences a slightly different degree of refraction when a heterogeneous light beam containing more than one frequency enters or leaves the medium. This effect is termed **dispersion** and is responsible for chromatic aberration in microscope objectives.

### Contributing Author

**Michael W. Davidson** - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.