# Measuring the Wavelength of Light

## Comsewogue High School WISE Project by Denise Simon & Andrea Cannizzaro Spring 2003 ## How did we do this?

To experimentally measure the wavelength of different colors of laser light, we used the process of diffraction and interference. Diffraction is the spreading of a wave behind a barrier and interference is the process by which the waves are split apart and then recombined. A similar experiment was performed by British scientist, Thomas Young in 1801. Young's experiment is called the "double slit experiment". Using a grating with two slits, Young was able to determine that light has wave like properties.

To find the wavelength of light, we shined a green laser pointer and a red helium-neon laser through a ronchi ruling (as shown in the picture below), which is a small piece of glass with bars in it, that will split up the laser beam. Next we traced the dots created by diffraction and interference on a piece of graph paper. The ronchi ruling was held in place, in front of the laser, at a distance 158 inches or 401.32 centimeters from the wall. This value will later be used as "L" or the distance from the grating to the observation point which is the graph paper in our case.

## The Ronchi Ruling

The first picture (on the left) is a close-up picture of the ronchi ruling sitting on a sheet of regular graph paper with 1/4" squares. As you can see the black lines are very uniform, and the width of the lines is nearly the same as the clear spaces between them. We could estimate the spacing between lines on the grating with this picture, but the results aren't very accurate because of the distortions in the picture.

A better method for measuring the line spacing was to use a little hand-held microscope that has a built-in scale. To see the scale clearly the Ronchi grating was set on an overhead projector that had a bright light. Using the microscope we were able to determine the spacing between the slits in the ronchi ruling to be very close to 0.010 inches or 0.025 centimeters, due to the fact that the spacings of the ruling matched the scale within the microscope. This value will be referred to as "d" when we analyze the results of our experiment.

## What were our Results?

To calculate the wavelengths of the two different lasers we needed to find the average spacing between the dots in each of the diffracted images. This value is referred to as "s", which for the green laser is 0.837 cm and for the red laser is 1.00 cm. "s"was obtained by measuring the total distance between many dots and then divided by the number of spaces between those dots. In our first trial, we divided by the number of dots rather than spaces, which resulted in an inaccurate reading.

Once all of our measurements were completed we were able to solve for the wavlength of light using the equation shown at the right above. We are able to use delta(theta) rather than sin(theta) due to the fact that the value for theta is extremely small and not relevant in the final outcome of s/L. Plugging in all of our experimental values into the equation we were able to find the wavelength of the red helium-neon laser to be 623x10-9 m or 623 nm and the wavelength of the green laser pointer to be 522x10-9 m or 522 nm. Usually the uncertainty in these results should be under 1%, however our results had a greater uncertainty, which was most likely due to difficulties measuring the spacing of the slits in the ronchi ruling.

The wavelengths of the red and green lasers of the type we used have been measured more precisely in other experiments to be 632.8 nm and 532 nm, respectively. So for the red laser our result is 1.5% smaller than the known value, and for the green laser our result is 1.9% too small. Since our result is too small by a similar amount in both cases, most likely the source for the errors is the measurement of the spacing between the slits in the ronchi ruling.

All in all our experiment verified the findings of Thomas Young when he proved light to be a wave due to the fact that it could be diffracted in such a manner.

## Want to Learn More?

5.Ronchi Rulings 3