A spectrometer only needs two items: a dispersive element and a screen. A dispersive element is anything that takes light and spatially separates it into its spectral components. A common dispersive element is a prism, as shown in Fig. 1, which works due to refraction. If you send white light into a dispersive prism, you will see a rainbow exiting because each spectral component refracts at a different angle. For a prism, the smaller the wavelength of light, the larger the refraction angle. So, blue light (λb = 400–490 nm) refracts at a larger angle than red light (λr = 620–750 nm). If you calibrate the prism so that you know at what angle each
Fig. 1 A dispersive prism takes white light, which enters the prism from the left, and makes a rainbow. Each wavelength is refracted at a different angle. The white light source I used to make this picture is a tungsten lamp.
Fig.2 (a) An example of white light, which is composed of many spectral components, reflecting off a reflection grating. For illustrative purposes, d, which is usually very small, is greatly enlarged. We also only show one order to keep the example a little cleaner. (b) An example of white light diffracting through a transmission grating. Again, d is greatly enlarged and we only show one order. (c) An example of blue light with λ = 455 nm hitting perpendicular to the transmission grating and being diffracted. In this example, we show all diffraction orders. The angles of diffraction are calculated using Eq.1 .
wavelength refracts, you can send in an unknown wavelength, measure the angle of refraction, and use math to determine the wavelength of the light. You can also send in light from, for example, a hydrogen lamp and see what wavelengths or spectral components are in that light. Knowing how each wavelength refracts allows you to determine what wavelengths make up the hydrogen lamp spectrum.
In spectroscopy, the most common dispersive element is an optical grating, which works due to diffraction. Optical gratings commonly come in two types: transmission and reflection, see Fig. 2. Either way, the optical grating is a dispersive element that will spatially separate light into its spectral components because each spectral component diffracts at a different angle.
To create the diffraction, both types of gratings have small structures separated by a distance d. A reflection grating has a bunch of small tilted mirrors called rulings while a transmission grating has a bunch of small slits. The only physical criterion for a grating is that d>λ. The size of d in Fig. 2 has been greatly enlarged for visual purposes. While d must be larger than λ, in practice we also make sure that d is typically less than about 5λ to ensure suitable diffraction angles.
We will start with the equations that describe how spectral components are diffracted through a transmission grating; we will find that each spectral component can be diffracted at multiple, but well defined, angles. The math behind the next equation is a little complicated, but the end result is really what we care about. Let’s start by keeping things simple and assume the incoming light is perpendicular to the grating, see Fig. 2c. The light diffracts through the grating according to the equation:
d sin θm = mλ (1)
for incident light perpendicular to a transmission grating
In this equation, d is the distance between the slits, m is an integer known as thediffraction order (the fact that a spectral component diffracts at multiple but well defined angles is mathematically represented by m), λ is the wavelength of a spectral component of the light, and θm is the angle of diffraction for order m. m can be a negative integer, zero, or a positive integer. If you know d and m, you can then measure θm and use that to calculate λ.
Example A transmission grating has
