# LIF - Optics and the Spectrometer

All pages in this lab

This experiment involves doing a bit of optics so you may need to brush up on a couple of ideas and learn a little about the spectrometers to get the best possible results. Watch the OPTICS video.

# Lenses

A lens is just pieces of glass with curved surfaces such that the directions of incoming rays of light are changed according to Snell's law $n_1\sin{\theta_1}=n_2\sin{\theta2}$ at each surface. For any lens, there is a particular distance for which light from a point source at that distance from the lens becomes collimated (i.e. all rays parallel) upon passing through the lens. This distance is the focal length.

An object is in focus when all rays emerging from any point on the object converge together in a point on the other side of the lens. This occurs for a lens of focal length f when $\frac{1}{o}+\frac{1}{i}=\frac{1}{f}$, where o is the distance from the source (or, object) to the lens and i is the distance from the lens to the image. In other words, if the lens is a distance o from the source, the image will be focused a distance i from the other side of the lens.

The size of the image created is sometimes important. For example, in this experiment, we would like for the image to cover the spectrometer slit. Consider the three rays drawn below between object and image:

By noticing similar triangles, we see that the ratio of the height of the image to the height of the object (i.e. the magnification) is given by: $M\equiv\frac{i}{o}=\frac{h_i}{h_o}$. In a multiple lens system, the total magnification is simply the product of the magnifications for each individual lens involved: $M_{tot}=M_1\times M_2\times M_3\times...\times M_n$.

# Spectrometer

In this experiment, you will use a spectrometer to measure the intensity of light as a function of wavelength. The spectrometer used in this experiment consists of multiple mirrors and a reflection grating as shown to the left. The mirrors collimate and refocus the light, and the grating spreads it out like a prism so that only light in a very small range of wavelengths will be focused on the exit slit at one time. When you turn the wavelength knob on top of the spectrometer, the grating turns and focuses a different range of wavelengths on the exit slit.

To get the best signal and the best resolution with the spectrometer, the most important factors are the following:

• The entrance and exit slits must be parallel--this affects mainly the resolution. It should not be a problem but if you are having excessive difficulty getting good results, you may want to check this.
• The full grating should be used. That is, it should be covered with the light. Since you can't see the grating itself, you have to make sure that it is covered by getting a large enough solid angle into the entrance slit. The spectrometer has an f number of 3.5 which means that the ratio of the distance from the final lens to the slit to the diameter of the lens must be less than or equal to 3.5 to make sure that the grating is filled. Basically, this means that your lens should be 15 cm or less from the spectrometer. We get around this in the absorption section of the experiment because the light is very intense.