Experiment 29: Interference Using a hand-held laser pointer and a diffraction grating consisting of threads making an elongated V pattern and mounted on clear plastic we observe the maxima created when the light is directed through the pattern at various separations, and with various incident angles. We determine the angular separation of the maxima and use this separation to estimate the wavelength of the light. We then use manufactured diffraction gratings to observe maxima with large separation and accurately determine the wavelength of the light. In your kit you will find a plate of clear plastic with several threads forming an elongated V pattern. I could not do this experiment because I do not have the plate of clear plastic with several threads forming an elongated V pattern in my lab kit. I understand this concept of the double slit experiment though. The threads are separated by a consistent distance at the top and should be separated by a consistent distance at any horizontal position below the top. If the separation is not consistent you may attempt to gently reposition some of the threads. Alternatively you can use either threads or long hairs to attempt to create your own V pattern. Orient the plate so that the V pattern is upright, with the widest spacing at the top. Shine the laser through the thread V near the top of the plate and onto a smooth wall at least 5 meters away. Gradually move the laser down through the V, so that it shines through threads that become closer and closer together. Observe what happens to the pattern on the wall. Continue moving down the V until you obtain the most distinct possible set of bright spots on the wall. Note the vertical position of the beam on the V (use the vertical ruler). As best you can, determine for this position the distance between the distinct bright spots formed on the wall. Measure the width of the V at this point, and the number of spaces between the threads across the width. Record also the distance to the wall. On the plastic plate, to the right of the V (if the V is on the side of the plate facing you) is taped a piece of what appears to be clear plastic. Place the screen on its side (so that the ruler is horizontal) a few cm on the other side of the plate and shine the light through the piece of 'clear plastic'. The beam will be split into three beams. Position the plate and the screen so that the three spots on the screen are equally spaced and span most of the width of the screen. Measure the distance from the plate to the screen. You should have measurements that will permit you to determine the angle at which the two 'split' beams diverge from the central beam. On the left of the V are taped pairs of pieces of apparently clear plastic at various angles to one another. Investigate the patterns formed on the screen when beams are passed through these pieces. Hold the plastic plate so that the 'clear plastic' pieces are as close as possible to a clear bottle full of colored water (e.g., a colored soft drink) and shine the laser through the pieces and into the soft drink. Observe the beam pattern. Analysis of results As a first approximation, when the separation of bright spots is small compared to the distance from the thread V to the wall, the separation `dy of the bright spots will be in the same proportion to the wavelength `lambda of the light as the distance d between the threads to the distance R to the wall (i.e., `dy / `lambda = d / R). Using your observed quantities, what do you obtain for the wavelength `lambda of the light coming from the laser? The accurate relationship between `dy, `lambda, R and d is d sin(`theta) = d * [ `dy / (`dy^2 + R^2) ] = n * `lambda, where n is an integer. The piece of 'clear plastic' is actually crossed by a large number of equally spaced, parallel microscopic lines which have the same type of effect on light as the threads in the V. From your data determine the angle `theta at which the 'clear plastic' piece caused the beams to the right and left to diverge from the central beam. For these beams we have n = 1, so that d sin(`theta) = `lambda. Given that `lambda is about 6.7 * 10^-7 meter, what is d? How many lines would we therefore have per cm? What therefore would we get for the angle `theta, if we had n = 2? What does this explain about what you saw when you shined the beam through the plastic?