Observation Screen. Introduction

Transcription

1 1 PHYS 1301 Diffraction Introduction Diffraction basically means `spreading out, while interference is a pattern that emerges when waves collide. You may have already seen a demonstration of interference with light waves of a certain color passing through 2 slits in the lecture section of the course. In today s lab, we will use light waves containing various colors to observe diffraction and interference by shining onto a large series of slits (apertures) that are separated from one another by a very small distance comparable to the wavelength of that wave. Such a series of apertures is called a diffraction grating. You will use interference measurements to then calculate the wavelength of visible light, a quantity that is far too small to measure directly or see with the naked eye. Wavefront Diffraction d crest trough n= 2 n = 0 n= n=1 Constructive Observation Screen If we imagine a light wave as similar to a water wave, with wavecrests (wavefronts) that move perpendicular to themselves, when a wavefront is incident upon the diffraction grating, parts of the wavefront are removed and each aperture serves as a source for a new wavefront that spreads out (diffracts). This is illustrated in the plan-view figure above. Since each of these sources is driven by the initial wave front, all the sources are in phase (meaning they all crest or trough at the same time when leaving their aperture). However, by the time the waves collide at some point on an observation screen behind the grating, they may be out of phase with one another. If all the peaks or all the troughs of the waves are still synchronized in time there, we say that at that point there is constructive interference. We see a bright region. If, on the other hand, the peaks of waves from some apertures are synchronized with the troughs of the other

2 waves, everything cancels out and we say that destructive interference occurred at that point. We see a dark region on the screen. The dashed directions in the diagram represent the angles of diffraction at which constructive interference takes place. The order n is the way to describe which of the above directions is involved (n=0, n=1, n=2, ) In this experiment, we will be observing the effect produced when light from a mercury lamp is passed through a diffraction grating. Such a lamp produces several colors of light, each of a different wavelength ; each color will have its own interference pattern with lines of different order n. A mathematical relationship can be derived which relates the wavelength, the angle of the particular diffraction, the distance between two consecutive slits d, and the order of diffraction n. This is called the diffraction equation: = d sin n Using the known value of d from the grating and measuring for a given order n, we can calculate for each color involved. Generally, the larger the wavelength the larger the angle of diffraction. This means that red light will be diffracted more than blue light. 2

3 3 Procedure & Equipment 1) Place one meter stick flat on the table with the metric scale up. Have one end of the stick be flush with the table edge (shown as Observer below) to make observation easier. Place a second meter stick on edge with the metric scale up, perpendicular to the other meter stick so as to make an L-shape. These meter sticks form the sides of a right-angled triangle that can be used to calculate the angles of diffraction. grating y Mercury Lamp Ͽ Caution! Don t touch the actual diffraction grating film you will damage it. 2) Position the grating (in its holder) perpendicular to and at one end of the 1 st meter stick. Caution! Take care when handling the lamp if the bulb breaks, the mercury vapor inside is highly poisonous. Take care when handling the lamp it uses a very high voltage, don t stick your fingers anywhere near the bulb ends. 3) Position the Mercury lamp on end at the corner of the L formed by the meter sticks, facing the grating; turn it on. Measure x, the fixed distance between the grating and lamp. 4) Your eye is going to be the observation screen. Place your eye on a level with the grating and look through it, back towards the lamp. Directly ahead, the light source should be visible; this is the n=0 image. Further to the right (or left) you should see iamges in the colors of violet, green, and yellow with violet closest to the center (diffracted the least). These 3 lines compose the first order diffraction (n = 1). Looking even farther out should reveal a second similar set of colored lines. This is the second order diffraction (n = 2). Trouble Shooting You may need to bring your eye closer to the grating Move your line of sight, not the grating The grating may not be oriented correctly in its holder take out and rotate by 90 0 Remove any other light source in your line of sight

4 4 5) For each colored line you see, measure y by guiding your partner to the positions along the 2 nd stick where you see the colored line image. Record color, order and y for each line. Analysis To find the wavelengths of the three observed colors, you will need to find the diffraction angle of the colors. After you have taken all your data, calculate the angle from the expression: = arctan (y/x) Arctan is the inverse of the tangent, also be written as tan -1, and may be found on the buttons of a simple calculator. The grating manufacturer tells us that the grating has apertures per inch. Use this calculate the distance d in mm (1 inch = 2.54 cm) between successive apertures. Use the diffraction equation given in the introduction to find the wavelengths of the different colors of the mercury spectrum. If you observed different orders n of diffraction, calculate the wavelengths of the same color for the different orders of diffraction. Caution: Units are important in this lab! Your values for the wavelength will be in the same unit (mm) as your number for the grating spacing.

5 5 Results Color n y x = d = Calculations: (Show units!) Questions 1. a) In general terms, how was related to the angle of diffraction? b) In general, how is related to the redness or blueness of the line? c) Was the calculated wavelength of a particular color significantly different for different orders of diffraction? 2. Calculate the percent errors for your wavelengths compared to the true values. Actual wavelength values: Violet: nm nm (there are actually 2 lines very close together) Green: nm Yellow: nm (1 nm = 10-9 meter) Conclusions