Microwave Diffraction and Interference Department of Physics Ryerson University rev.2014 1 Introduction The object of this experiment is to observe interference and diffraction of microwave radiation, and to use the observations to measure the wavelength of the microwaves. The absorption of microwaves by materials will also be observed. Microwaves are electromagnetic waves which have wavelengths in the λ 1mm 30cm range, with corresponding frequencies ν 10 9 3x10 1 1Hz. They can be generated with a vacuum device known as a klystron, a solid state device called a Gunn oscillator, and by a magnetron, used in domestic ovens and high power transmitters. Here, we will use a Gunn oscillator to explore the wave properties of microwaves through double and single slit experiments, as well as their absorption by materials. 1.1 Equipment Gunn Diode Microwave Transmitter, ν = 10.525GHz, λ = 2.85cm Microwave Receiver Goniometer 2 x metal reflector, 1 narrow slit spacer Magnetic component holder Slit Extender Arm paper towel 1.2 Precautions The intensity of the microwave beam emerging from the microwave horn is within the limits of what is considered safe. However, to be on the safe side, avoid any unnecessary exposure of any part of your body to the radiation. It is especially advisable not to expose your eyes to the source of the microwaves at close range. 1
2 Double Slit Interference The objective of this part of the experiment is to observe the interference of microwaves and to use these observations to find their wavelength. Microwaves spreading out from a single source can be divided by openings in a metal screen. The beams coming from the two openings are coherent, will spread out (diffract) and interfere with each other. For some locations the interference will be constructive and for others it will be destructive with gradual changes from constructive to destructive in between. The type of interference is seen to depend on the angle, θ, at which the waves are observed. The angle is measured with respect to the centre line drawn through the midpoint between the two openings in the screen and perpedicular to the screen. The values of the angles for which constructive interference should be observed are given by the following equation: d sin θ = mλ (1) where d is the centre to centre space between the screen openings, λ is the wavelength of the waves, and m is a positive integer (m = 0, 1, 2,...). 2.1 Procedure 1. Obtain the goniometer with microwave transmitter and receiver mounted at either end. The transmitter should be mounted on the fixed arm of the goniometer, at least 30 cm from the centre. The reciever should be mounted on the movable arm of the goniometer, as far from the centre as possible. The movable arm should be at 180. 2. Set the small metal sheet at the centre of the magnetic mount, and one of each of the other larger metal plates on each side. Adjust the spacing such that the spacing is roughly 1.5 cm, with the same slit spacing on either side. Ensure the slits are oriented perpendicular to the lab bench. Ensure the magnetic component holder is aligned perpendicular to the microwaves. 3. Plug in your transmitter and turn on your reciever to the 30x range. Your reciever has 4 ranges. If you read a current in the 30x range, you need to multiply the reading by 30x in order to get the actual value. There is a variable sensitivity knob. If you need to adjust the variable sensitivity knob, do not adjust it for the remainder of the measurement. Adjust the multiplier of the reciever until it reads 80% of full scale. If 1x does not give sufficient signal, you can use the variable sensitivity to acheive a sufficient signal. 4. Quickly survey the range over which you will take data (120 to 240 to verify your diffraction pattern looks approximately as expected. Request assistance from your 2
TA if you are not seeing the approximate expected pattern of maxima and minima before proceeding. 5. Record receiver meter readings as a function of angle up to 60 on both sides of the centre, at 2 intervals. 6. Measure the centre to centre separation d of the two openings in the screen. 2.2 Analysis Plot the intensity data as a function of angle θ with a smooth curve between points. Determine the angle separating each side maximum from the centre maximum and average. Estimate the uncertainty in this angle. Use Equation 1 and the average location of the maxima to get an estimate of the microwave wavelength and the uncertainty of this value. Compare and comment on the specified value for the Gunn Transmitter. Does your range of uncertainty include the manufacturer s value for wavelength? 3 Single Slit Diffraction The image of a point source passing through a small opening can be characterized as a fuzzy central image surrounded by concentric fuzzy bands of light. The angular separation, θ, of the first minima (dark space) is inversely related to the size of the opening, a, and proportional to the wavelength λ: sin θ = k λ a (2) where k is a constant of proportionality which depends slightly on the shape of the opening. For a rectangular opening, k = 1, but for a circular opening, k = 1.22. The objective is to observe the single slit diffraction pattern and obtain a rough estimate of the wavelength of the microwave source. 3.1 Procedure 1. Using the two large metal screens, create a 1.5 cm opening, mounted in the middle of the magnetic component holder. The reciever should again be as far from the screen as possible. Adjust the sensitivity such that the central maxima gives roughly 80% of full scale. 2. Record receiver meter readings as a function of angle up to 60 on both sides of the centre, at 2 intervals. 3. Repeat steps 1 and 2, using a slit width of 6 cm. 3
3.2 Analysis Plot relative power versus angle for both the 1.5 cm slit and 6 cm slit on the same graph as the double slit. Comment on any similarities between the two patterns. Estimate the angular separation of the minima, if they are present, on either side of the central maximum for each pattern, including the uncertainty in these minima. Note that the larger opening results in a narrower pattern of received power. If possible, estimate the wavelength of the microwaves using Equation 2 for single slit diffraction and the uncertainty. Compare to the stated wavelength for the Gunn diode. Does your range of uncertainty include the manufacturer s value for wavelength? 4 Absorption of Microwaves by Wet and Dry Materials The object of this part of the experiment is to observe the ability of water to absorb microwaves. 4.1 Procedure 1. Adjust the reciever to 180 and the recieved power to 80% of full scale. Remove the magnetic mount. 2. Record the meter reading with no material between the transmitter and receiver. 3. Crumple a paper towel and place in the receiver horn. Record the meter reading. 4. Remove the paper towel from the horn and wet it. The towel should be damp but not dripping. Place the damp towel in the receiver and record the new meter reading. 5. Try other types of materials as available: plastics, cloth, etc. 4.2 Analysis Compare the reading of the wet and dry paper towels, and any other types of material you may have used. What can you conclude from these observations? 4
References [1] Instruction Manual and Experiment Guide for the PASCO Scientific Model WA-9314B, PASCO Scientific, 1991. 5