This demo arises from my desire to synthesize and communicate the fact that emission and absorption spectra are two sides of the same coin. This is usually mentioned in textbooks in the form of a spectroscopy setup of light going through a gas and being emitted by the same gas, with their corresponding spectra (e.g. Figure 39.18 from the intro book from Young and Freedman). However, the truth of the matter is that, to my knowledge, this experiment is not a standard demonstration in physics curricula, and it seems to be a rather complicated thing to set up, and more so with a pedagogical focus in mind. In introductory courses, students don't see explicitly where these spectra come from since they don't possess the mathematical tools to derive them, and current labs and demos work mostly with emission spectra lamps, while an absorption spectra experiment seems to be lacking. The link between absorption and emission is usually briefly mentioned, but I know of no experiment that explores the absorption and emission spectra of one substance and demonstrates that they are complementary (i.e. that the peaks occur at the same wavelengths).

The demonstration will attempt to bridge the gap between absorption and emission spectra using a rather simple diffraction grating spectrometer setup to measure wavelengths and salt flames as absorption/emission substances. Indeed, studying the color of the flames that are produced when a salt is burned is a common experiment in the chemistry curriculum. It is also one of the experiments that contributed to the development of absorption and emission spectra theory a few centuries ago, when scientists postulated that the color of the sparks made by burning metals were unique to the metals being burned. Using salt flames as the light source could thus link a historical motivation to the experiment and the demo can even serve as a way to introduce the concept in the first place, provided students have already learned about lenses and diffraction theory.

The experiment consists of a flame source, a salt that is burned, a white light source, and three spectrometers. One spectrometer will measure the emission spectrum of the flame, one will measure the spectrum of the white light source, and the other will measure the spectrum of the white light source after it has passed through the salt flame in order to measure the flame's absorption spectrum (this last step was inspired by this article).

The figure below shows the optical schematic of the setup. A collimated white light source is sent through a 50:50 beamsplitter ($BS$) that separates the beam in two. The transmitted beam is sent through lens $L_3$, which focuses the light onto a flame from a Bunsen burner. This beam is later recollimated by $L_4$. The mirror $M$ reflects the light and sends it through $L_1$ and $L_2$, which also focus and recollimate the light; while technically not necessary if the beam is perfectly collimated in the first place, this is rarely the case and these lenses serve to minimize beam divergence over longer distances. Both $M$ and $BS$ as well as the white light source can be mounted on kinematic mounts to facilitate alignment of the beam trajectories. A fifth lens, $L_5$, is added and positioned so that its focus is at the flame's location in order to capture the light from the flame. All lenses serve to have all light beams entering the spectrometers are collimated.

Figure 1.1: Optical setup for this experiment. Some preliminary dimensions and specifications of the components are highlighted.

Figure 1.2: Spectrometer design. Collimated light is sent through a slit. An aspheric lens is positioned such that its focus is at the slit position in order to get a collimated rectangular beam of light. This beam is then sent through a grating and the first order diffracted light is imaged with a web camera for later analysis.

The spectrometer consists of a slit ($S$) through which the collimated light beams enter. An aspheric lens focused at the slit position would then recollimate the light emanating from the slit, which will be diverging as it will diffract significantly at the edges. I chose an aspheric lens in order to minimize spherical aberrations going into the grating and thus increase resolution of individual wavelengths. The collimated light from the slit is then sent through a 830 groove/mm diffraction grating that separates the light into its constituent colors. After the grating, a wide angle webcam is positioned so that the first order diffraction maxima of the wavelengths are captured. For white light ($\lambda = 400\sim700 \text{ nm}$) at incident angle $\theta_i = 0$, the first order diffraction will occur at $\theta^\lambda_{m=1} = 19.4\sim35.5 \text{ deg}$. Figure 1.2 shows the spectrometer setup in detail. I am still deciding on the length between the slit and the grating, but I am thinking of about 4 inches, using a lens tube to ensure that the slit and the lens are coaxial and putting the grating just after the tube.