Light travels in a straight line through a uniform medium. When light passes from one transparent material into another, it changes direction, a phenomenon called refraction. This bending occurs because the speed of light differs in various substances, causing the wave front to pivot as it transitions between media. The index of refraction (\(n\)) quantifies this change in speed and the resulting degree of light bending. This value is used by scientists and engineers for designing lenses, fiber optics, and other optical instruments.
Understanding the Index of Refraction
The index of refraction measures a material’s optical density relative to a vacuum. It describes how much a medium slows down light compared to its speed in empty space. A higher index indicates greater optical density, meaning light travels slower through that medium.
A vacuum is the only environment where light reaches its maximum speed, so its index of refraction is defined as exactly 1.0. All other transparent materials have an index greater than 1.0, meaning light is always slower within them. For example, the index for air is approximately 1.0003, while water is about 1.33, and common glass ranges from 1.5 to 1.6. The difference between the indices of two materials determines the extent of refraction when light crosses their boundary.
Calculation Based on Wave Speed
The most direct method for determining the index of refraction involves comparing light speeds. The index \(n\) is calculated as the ratio of the speed of light in a vacuum (\(c\)) to the speed of light (\(v\)) as it travels through the specific medium. This relationship is expressed by the equation \(n = c/v\).
The speed of light in a vacuum (\(c\)) is a universal constant, approximately \(3.00 \times 10^8\) meters per second. The variable \(v\), the phase velocity, is the speed at which the light wave propagates through the material. For example, if light travels through freshwater at \(v = 2.25 \times 10^8\) m/s, the index \(n\) is \(1.33\) (\(3.00 \times 10^8 \text{ m/s} / 2.25 \times 10^8 \text{ m/s}\)).
Since \(v\) can never exceed \(c\), the ratio \(c/v\) is always 1 or greater, confirming that the index of refraction is never less than one. While this method defines the absolute index, it is primarily conceptual because accurately measuring the speed of light in a material is difficult.
Calculation Based on Angles of Refraction
For practical laboratory measurements, the index of refraction is determined by measuring the angles of a light ray as it crosses a boundary. This method relies on Snell’s Law, which mathematically relates the indices of refraction of the two media and the angles of the light ray: \(n_1 \sin\theta_1 = n_2 \sin\theta_2\).
In this formula, \(n_1\) and \(n_2\) are the indices for the first and second media. The angles \(\theta_1\) (incidence) and \(\theta_2\) (refraction) must be measured relative to the normal line, which is perpendicular to the surface boundary. \(\theta_1\) is the angle the incoming ray makes with the normal, and \(\theta_2\) is the angle the bent ray makes after crossing the boundary.
To find an unknown index, such as \(n_2\), the equation is rearranged: \(n_2 = n_1 (\sin\theta_1 / \sin\theta_2)\). For example, if light travels from air (\(n_1 \approx 1.00\)) into an unknown liquid, \(n_2\) is found by measuring \(\theta_1\) and \(\theta_2\). This technique is useful because it only requires measuring angles, often done using goniometers or refractometers. If light moves from a less dense medium (\(n_1\)) to a more dense medium (\(n_2\)), the ray bends toward the normal, meaning \(\theta_2\) will be smaller than \(\theta_1\).
Variables That Influence the Index
The index of refraction is not a perfect constant and can be influenced by several physical variables. One significant factor is the specific wavelength of light being used, a phenomenon known as dispersion.
Wavelength (Dispersion)
The index changes depending on the color of light. Shorter wavelengths, such as blue or violet light, experience a slightly higher index and bend more than longer wavelengths like red light. This variation explains why a prism separates white light into a spectrum of colors. Due to dispersion, a standard wavelength must be specified when reporting an index; the yellow light from a sodium lamp (D-line at 589 nanometers) is the most frequently used reference standard.
Temperature and Pressure
Temperature and pressure also have a measurable effect on a material’s index. An increase in temperature typically causes a substance to expand and become less dense, allowing light to travel slightly faster. This faster speed results in a small decrease in the index of refraction. Conversely, increasing the pressure on a material, especially a gas, increases its density and leads to a minor increase in the index.