The refraction of visible light is an important characteristic of lenses that allows them to focus a beam of light onto a single point. Refraction (or bending of the light) occurs as light passes from a one medium to another when there is a difference in the index of refraction between the two materials, and is responsible for a variety of familiar phenomena such as the apparent distortion of objects partially submerged in water.

Refractive index is defined as the relative speed at which light moves through a 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. The index of refraction, N (or n), of other transparent materials is defined through the equation:

where c is the speed of light, and V is the velocity of light in that material. Because the refractive index of a vacuum is defined as 1.0 and a vacuum is devoid of any material, the refractive indices of all transparent materials are therefore greater than 1.0. For most practical purposes, the refractive index of light through air (1.0003) can be used to calculate refractive indices of unknown materials. Refractive indices of some common materials are presented in Table 1 below.

Material Refractive Index Air 1.0003 Water 1.33 Glycerin 1.47 Immersion Oil 1.515 Glass 1.52 Flint 1.66 Zircon 1.92 Diamond 2.42 Lead Sulfide 3.91

Table 1

When light passes from a less dense medium (such as air) to a more dense medium (such as water), the speed of the wave decreases. Alternatively, when light passes from a more dense medium (water) to a less dense medium (air), the speed of the wave increases. The angle of refracted light is dependent upon both the angle of incidence and the composition of the material into which it is entering. We can define the normal as a line perpendicular to the boundary between two substances. Light will pass into the boundary at an angle to the normal and will be refracted according to Snell's Law:

Where N represents the refractive indices of material 1 and material 2 and q 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 smaller than the angle of incidence. Alternatively when N(2) is greater than N(1) the angle of refraction is always greater than the angle of incidence. When the two refractive indices are equal (N(1) = N(2)), then the light is passed through without refraction. The concept of refractive index is illustrated below for the case of light passing from air through both glass and water. Notice that while both beams enter the denser material through the same angle of incidence with respect to the normal (60 degrees), the refraction for glass is almost 6 degrees more than that for water due to the higher refractive index of glass.

Scientists have found that the index of refraction varies with the frequency of radiation (or wavelength) of light. This is occurs with all transparent media and has been termed dispersion. As the wavelength of light increases, the refractive index decreases. It is the dispersion of light by glass that is responsible for the familiar splitting of light into its component colors by a prism.

When measuring the refractive index of a transparent substance, the particular wavelength used in the measurement must be identified. This is because dispersion is wavelength-dependent as illustrated in Table 2 showing dispersion of three independent wavelengths in various media.

Material Blue (486.1 nm) Yellow (589.3 nm) Red (656.3 nm) Crown Glass 1.524 1.517 1.515 Flint Glass 1.639 1.627 1.622 Water 1.337 1.333 1.331 Cargille Oil 1.530 1.520 1.516 Carbon Disulfide 1.652 1.628 1.618

Table 2

The most commonly used wavelength to measure refractive index is that emitted by a sodium lamp, which has a strong and closely spaced doublet having an average wavelength of 5.893 nanometers. This light is termed the D line spectrum, and represents yellow light listed in Table 2 above. Likewise F line and C line spectra correspond to blue and red light of specific wavelengths (also represented in Table 2) emitted by hydrogen. It is apparent that as the wavelength of light is increased from 486.1 nanometers (blue or F line) to 656.3 nanometers (red or C line), the refractive index of light through a particular medium decreases. Dispersion can be quantitatively defined as:

where n is the refractive index of the material at a particular wavelength designated by D, F, and C, which represent the spectral lines of sodium and hydrogen as discussed above. Many factors play a role in the dispersion of various materials including the elemental and molecular composition. Several inorganic solids having unusually high dispersions are chromates, dichromates, cyanides, vanadates, and halide complexes. Organic substituents can also contribute to high dispersion as evidenced by the extremely high dispersion values found with materials having a cinnamyl moiety.

For a virtual demonstration of light refraction, please visit our interactive Java tutorial that explores the effect of incident angle and wavelength on refraction of light when it passes into a medium of greater refractive index.

	Interactive Java Tutorial
Refraction of Light Discover how a beam of light is "bent" by refraction when it passes from one medium into another. Adjust the incident angle and color of the light wave and observe the effect these changes have on refraction.

The relative position of the object with respect to the front focal point of the lens determines how the object is imaged. If the object is beyond twice the length of the focal point, then it appears smaller and inverted and must be imaged by an additional lens in order to magnify the size. However, when the image is closer to the lens than the focal point, the image appears upright and larger, as can be easily demonstrated with a simple magnifying glass. For a demonstration of refraction and imaging by lenses, check our our interactive Java tutorials on convex, concave and infinitely configurable lenses.

	Interactive Java Tutorial
Image Magnification Explore how the image of a giraffe is magnified by refraction of light waves passing through a simple thin bi-convex lens.

One of the most common optical illusions due to refracted light is nicely demonstrated by visualizing objects in water. Light is refracted when it leaves water giving rise to the illusion that objects in water appear to be closer than they really are. An excellent example is provided in the illustration below (Figure 3) using a drinking straw placed in a glass of water.

The straw appears magnified and slightly distorted due to refraction of reflected light waves from the surface of the straw. The waves must first pass through the water then through the glass/water boundary and finally through the air. Light waves coming from the ends (front and back) of the straw are shifted to a greater degree than those coming from the center of the straw, making it appear larger than it really is.

This phenomenon can be used to determine the refractive index of a liquid with an optical microscope. A flat cell capable of holding liquid with a mark (or graduations) placed on the inside glass surface is constructed (or purchased) for this experiment. One of the microscope eyepieces must have a graduated reticle inserted at the primary image plane for line width measurements of the mark in the flat cell. Before adding the liquid of unknown refractive index to the cell, the microscope is focused on the mark at the bottom of the cell and a measurement of the mark's position on the reticle is noted. Next, a small amount of liquid is added to the cell and the microscope is refocused on the mark (through the liquid) and a new measurement is taken. The microscope is finally focused on the surface of the liquid, and a third reading is recorded by measuring the position of the mark on the reticle. The refractive index of the unknown liquid can then be calculated using the following equation:

where D(measured) is the measured depth (from the surface of the liquid to the position of the mark on the empty cell) using the microscope and D(apparent) is the mark measurement with and without liquid.

When light passes through a medium of high refractive index into a medium of lower refractive index, the incident angle of the light waves becomes an important factor. If the incident angle increases past a specific value (dependent upon the refractive index of the two media), it will reach a point where the angle is so large that no light is refracted into the medium of lower refractive index, as illustrated in Figure 4. In this figure, individual light rays are represented by either red or yellow colored arrows moving from a medium of high refractive index (N(2)) to one of lower refractive index (N(1)). The angle of incidence of each individual light ray is denoted by i and the angle of refraction by r. The four yellow light rays all have an angle of incidence (i) low enough to pass through the interface between the two media. However, the two red light rays have incident angles that exceed the critical angle (approximately 41 degrees) and are reflected either into the boundary between the media or back into the high refractive index medium.

This phenomenon takes place when the angle of refraction (angle r in Figure 4) becomes equal to 90 degrees and Snell's law reduces to:

where (q) is now termed the critical angle C, and if the medium of lesser refractive index is air (n = 1.00), the equation reduces to:

When the critical angle is exceeded for a particular wave, it exhibits total reflection back into the medium. This concept is important in optical microscopy and will be discussed in greater detail in our discussion on immersion media in the Anatomy of the Microscope section of the Microscopy Primer.

Another important feature of light refraction, as discussed above, is that the wavelength of light has an impact on the amount of refraction in the same material. The amount of refraction is inversely proportional to the wavelength. Thus, shorter wavelength visible light is refracted at a greater angle than longer wavelength light. White light is composed of all the colors in the visible spectrum. When this light is passed through a glass prism, the white light is dispersed into its component colors in a manner that is dependent upon the individual wavelengths.

Dispersion is also responsible for chromatic aberration, an artifact resulting from refractive index variation with wavelength. When white light is passed through a simple convex lens, several focal points arise in close proximity that correspond to the minor refractive index differences of the component wavelengths. This effect tends to produce colored (either red or blue, depending upon focus) "halos" surrounding the images of objects. Correction of this aberration is accomplished by the use of combinations of two or more lens elements composed of materials having different dispersive properties. A good example is an achromatic lens constructed with both crown and flint glasses.

	Interactive Java Tutorial
Refraction by a Prism Examine how white light is separated into its component colors by refraction through the various angles in a prism. Adjust the incident angle and beam thickness and observe the effects on refraction.

Low frequency visible light (600 nanometers and greater) is refracted at a smaller angle than higher frequency light. Thus, when one views dispersed light from a prism, we see a rainbow-like effect where the component frequencies are split according to wavelength. This concept can be more thoroughly explored using our interactive Java tutorial that allows the student to change the incident angle and beam thickness of white light striking a prism.

Many devices make use of the fact that light can be refracted, reflected, and focused. The most common example is a camera, which is designed to create sharp and focused images onto an emulsion of film or the surface of a charge-coupled device (CCD) to produce an accurate image. Other optical devices include microscopes and telescopes that allow us to view details that are invisible to the unaided human eye, regardless of whether they are located on the head of a pin or in a distant galaxy.