Have you ever wondered how scientists can accurately measure the size of very small objects like molecules, nanoparticles, and parts of cells? Scientists are continually finding new ways to do this, and one powerful tool they use is light scattering. When an incoming beam of light hits an object, the light "scatters," or breaks into separate streams that form different patterns depending on the size of the object. This incoming light might be visible light, like the light we see from the sun, or it might be higher-energy light like X-rays.
The size of object each type of light can measure depends on the wavelength of the light, which is related to its energy. Larger, lower-energy wavelengths like the colors of visible light can be used to measure larger objects that are visible with the naked eye, while smaller, higher-energy wavelengths like X-rays can be used to measure extremely small objects. National labs like Argonne National Lab outside Chicago operate big X-ray machines that can measure the size of polymers, nanoparticles and other nanometer-scale structures. The light commercial laser pointers emit, on the other hand, is the perfect wavelength to measure the size of a human hair using the same method, outlined below.
This activity was adapted from: https://www.sciencenewsforstudents.org/blog/eureka-lab/measure-width-your-hair-laser-pointer
- Cardboard piece larger than 2 in x 2 in
- Scotch tape
- Red and green laser pointers (you will need to note the wavelength of the laser pointers)
- Hair from students’ heads
To prepare a frame for the hair, cut a hole in the piece of cardboard, where the hole is approximately 2 inches x 2 inches (or smaller if students have short hair). Pull out a piece of hair ~5 cm long, or as long as you can if your hair is shorter than this. Tape the hair at the top and bottom of the cardboard frame, making sure it is tight and in the middle of the cutout.
Place the hair sample between the laser pointer and the wall so that the laser pointer beam is hitting the hair directly. You will see a scattering pattern on the wall when you reach this point. Δθ, which you will calculate later, is called the scattering angle.
Mark the scattering bands on the wall using both the red and green laser pointer, keeping track of which bands correspond to which color.
Measure h, the distance between centers of adjacent scattering bands, as shown.
Measure d, the distance between the hair and the wall where the scattering pattern appears.
Calculate the diameter of the hair using the calculations shown in the image. You will do a separate calculation for the red light and the green light, but the results you obtain should be approximately equal. Why do you think this is?
We can directly measure the distance between the hair and the wall, and the distance between adjacent scattering bands. Once we have this information, we can use geometric relationships to calculate the scattering angle. The scattering angle depends in a predictable way on two other variables—the wavelength of light used and the size of the object the light bounces off. If we know any two of these three quantities, we can calculate the third; in this case, we know the wavelength of light from the information provided on laser pointer, and we know the scattering angle from our own measurements and calculations, so we can use this information to determine the size of the object.
To see a demonstration of this activity and how it works, check out the video below from Jefferson Lab!