In this laboratory you will become familiar with a spectrometer and use it to study one of the basic properties of transparent media, the index of refraction. These instructions assume some familiarity with reflection, which is used here in particular.

For this lab, we may consider light as a collection of rays that travel in straight lines in a homogeneous transparent medium. The rays bend when they pass from one medium into another, a phenomenon termed refraction. In 1621, the Dutch scientist Willebrord Snell discovered an empirical law governing refraction. At the point where a light ray strikes the boundary between two media, draw a line perpendicular to the surface called the normal to the surface (see Figure 1). The angle between the incident ray and the normal is the angle of incidence \(\theta_{1}\), and the angle between the refracted ray and the normal is the angle of refraction \(\theta_{2}\). Snell’s law states that the incident ray and the refracted ray lie in the same plane, and that the angles are related by $$n_{1}\sin\theta_{1}=n_{2}\sin\theta_{2},$$ where \(n_{1}\) and \(n_{2}\) are the indices of refraction of the two media. The index of refraction \(n\) depends on the medium and also on the wavelength of the light (except in a vacuum, in which \(n=1\) for all wavelengths), a phenomenon termed dispersion.

By applying Snell’s law to two sides of a prism, one may determine the angle by which the emergent ray is deviated with respect to the incident ray (see Figure 2). The angle of deviation \(\delta\) depends on the index of refraction \(n\) of the prism, the angle \(\theta_{p}\) between the two faces of the prism, and the direction of the incident ray. By rotating the prism, one empirically finds that there is a unique orientation for which the angle of deviation is minimized. This occurs when the emerging ray makes the same angle with its normal as the incident ray makes with its normal. Using this fact, one may show that $$n=\frac{\sin\left(\frac{\theta_{p}+\delta_{m}}{2}\right)}{\sin\left(\frac{\theta_{p}}{2}\right)},$$ where \(\delta_{m}\) is the angle of minimum deviation. As you will discover, it is easy to determine the angle of minimum deviation experimentally.

In this lab a prism will be used to separate out the constituent wavelengths of a discrete light source (a low pressure mercury lamp) and you will use the spectrometer to measure the angle of minimum deviation for each wavelength (color). The equation above will then be used to determine the index of refraction of the prism.

Equipment Data Collection and Analysis Summary Questions