Refraction occurs as light passes from one medium to another only when there is a difference in the index of refraction between the two materials. The effects of refraction are responsible for a variety of familiar phenomena, such as the apparent bending of an object that is partially submerged in water and the mirages observed on a dry, sandy desert. The refraction of visible light is also an important characteristic of lenses that enables them to focus a beam of light onto a single point. This interactive tutorial explores how changes to the incident angle and refractive index differential between two dissimilar media affect the refraction angle of light at the interface.
The tutorial initializes with an incident beam of white light (represented by a yellow sine wave) passing from air into a second medium (crown glass is the default substance) of higher refractive index. Due to the phenomenon of dispersion, the white light is refracted at a variety of angles as a function of the individual component wavelengths comprising the incident beam. It is the dispersion of light by glass that is responsible for the familiar splitting of light into its component colors by a prism. In the tutorial, dispersion is simulated by overlapping sine waves having the various colors present in visible light (blue, green, red, purple, orange, and yellow). At initialization, the refraction angles for the white light component wavelengths vary between 33.39 and 33.91 degrees (for an incident angle of 58 degrees—the default setting). The angle of light passing from air to the second medium can be altered using the Incident Angle slider. As the slider is translated to the left and right, the refraction angle range is continuously updated and displayed in the tutorial window.
The wavelength spectrum of incident light in the tutorial can be changed from white to monochromatic using the radio buttons in the lower left-hand corner of the window. Activating the Monochromatic radio button simultaneously activates the Wavelength slider to enable changing the wavelength of light as well as the incident angle. A palette of materials having differing refractive indices is available in the Choose A Material pull-down menu. The refractive index value of each material is provided in the palette menu. The refractive index of the upper medium in the tutorial (air) is fixed at 1.0002, and the incident angle range is zero (normal to the interface) to 80 degrees for both white and monochromatic light.
As light passes from one substance into another, it will travel straight through with no change of direction when crossing the boundary between the two substances head-on (perpendicular, or a 90-degree angle of incidence). However, if the light impacts the boundary at any other angle it will be bent or refracted, with the degree of refraction increasing as the beam is progressively inclined at a greater angle with respect to the boundary. As an example, a beam of light striking water vertically will not be refracted, but if the beam enters the water at a slight angle it will be refracted to a very small degree. If the angle of the beam is increased even further, the light will refract with increasing proportion to the entry angle. Early scientists realized that the ratio between the angle at which the light crosses the media interface and the angle produced after refraction is a very precise characteristic of the material producing the refraction effect.
The refractive index of a transparent substance or material is defined as the relative speed at which light moves through the material with respect to its speed in a vacuum. By convention, the refractive index of a vacuum is defined as having a value of 1.0, which serves as a universally accepted reference point. The index of refraction of other transparent materials, commonly identified by the variable n, is defined through the equation:
where c is the speed of light in a vacuum and v is the velocity of light in the material. Because the refractive index of a vacuum is defined as 1.0, and light attains its maximum speed in a vacuum (which is devoid of any material), the refractive index of all other transparent materials exceeds the value of 1.0, and can be measured by a number of techniques. For most practical purposes, the refractive index of air (1.0003) is so close to that of a vacuum that it can be employed to calculate refractive indices of unknown materials. Materials with higher refractive indices slow the speed of light to a greater degree than those with lower refractive indices. In effect, these materials are said to be more refractive, and they exhibit a larger angle of refraction for incoming light rays passing through an air interface.
Although reference is usually made to a standard and fixed refractive index for a substance, careful measurements indicate that the index of refraction for a particular material varies with the frequency (and wavelength) of radiation, or the color of visible light. In other words, a substance has many refractive indices that may differ either marginally, or to a significant degree, as the color or wavelength of light is changed. This variation occurs for all transparent media and has been termed dispersion. The degree of dispersion exhibited by a specific material is dependent upon how much the refractive index changes with wavelength. For any substance, as the wavelength of light increases, the refractive index (or the bending of light) decreases. In other words, blue light, which comprises the shortest wavelength region in visible light, is refracted at significantly greater angles than is red light, which has the longest wavelengths. As discussed above, it is the dispersion of light by ordinary glass that is responsible for the familiar splitting of light into its component colors by a prism.