Lab 2 - Microwave Interference & Diffraction -F23

Toronto Metropolitan University - PCS213 Distribution, sale or profit without the authorization of the owner of this material is expressly prohibited Microwave Diffraction and Interference Physics Topics If necessary, review the following topics and relevant textbook sections from Serway / Jewett “Physics for Scientists and Engineers”, 10th Ed. • The Spectrum of Electromagnetic Waves (33.7) • Double-Slit Experimentation (36.1, 36.2, 36.3) • Diffraction Patters (37.1, 37.2, 37.3) Introduction The objective 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 ∼ 1 mm − 30 cm range, with corresponding frequencies ν ∼ 10 9 − 3 · 10 11 Hz . They can be generated with a vacuum device known as a klystron, a solid state device called a Gunn oscillator, or 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. Pre-Lab Questions Pre-lab questions are to be submitted at the start of your lab session. Your lab teaching as- sistant may review these questions with you during your lab session. Note: Pre-lab questions are to be submitted individually. 1.) Conceptually do you expect the results of this experiment to differ from a typical double slit experiment, where a wavelength in the visible spectrum is used? Explain your reasoning. 2.) Using a wavelength of λ = 2 . 85 cm , a slit separation of d = 5 cm and a slit width of a = 1 cm . (a) Determine the location of the first order interference peaks (ignoring diffraction) on an infinitely long screen placed 20 cm from the slits. (b) Generally when the interference (1) and diffraction (2) equations are discussed Page 1 of 7

Toronto Metropolitan University - PCS213 Distribution, sale or profit without the authorization of the owner of this material is expressly prohibited a small angle approximation is applied, is this approximation still valid when working this system? 3.) Microwave absorption: Based on your knowledge of microwaves, how do you expect them to be absorbed in comparison with visible light? Apparatus • Gunn Diode Microwave Transmitter, ν = 10 . 525 GHz , λ = 2 . 85 cm • Microwave receiver • Goniometer • 2x metal reflector, 1 narrow slit spacer • Magnetic component holder • Slit extender arm • Paper towel (a) Double Slit Interference Equipment Setup (b) Double Slit Interference Schematic Figure 1: Double Slit Interference, from [1] 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 Double Slit Interference Theory The objective of this part of the experiment is to observe the interference of microwaves and to use these observations to find their wavelength. Page 2 of 7

Toronto Metropolitan University - PCS213 Distribution, sale or profit without the authorization of the owner of this material is expressly prohibited (a) Single Slit Diffraction Equipment Setup (b) Single Slit Diffraction Schematic Figure 2: Single Slit Diffraction. Modified from [1]. 6.) Measure the centre to centre separation d of the two openings in the screen. Analysis Plot the intensity data as a function of angle ( θ ) with a smooth curve between points. De- termine the angle separating each maxima from the central maximum. Average the angular separations based on maxima order( m ), estimate the uncertainty in these average separa- tions. Use Equation 1 and the average maxima locations to get an experimental value of the source wavelength (including uncertainty). Compare and comment on the specified value for the Gunn Transmitter. Does your range of uncertainty include the manufacturer’s value for wavelength? 2 Single Slit Diffraction Theory 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 : sinθ = 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. Page 4 of 7

Toronto Metropolitan University - PCS213 Distribution, sale or profit without the authorization of the owner of this material is expressly prohibited Procedure 1.) Using the two large metal screens, create a 1.5 cm opening, mounted in the middle of the magnetic component holder. The receiver 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 5 ◦ intervals. 3.) Repeat steps 1 and 2, using a slit width of 6 cm. Analysis Create a new plot of relative power versus angle for both the 1.5 cm and 6 cm single slit. 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. Add the double slit data to this plot, comment on any similarities between the two patterns. Note that the larger opening results in a narrower pattern of received power. If possible, estimate the wavelength of the microwaves using Eqn. 2 for single slit diffraction. Compare to the stated wavelength for the Gunn diode. Does your range of uncertainty include the manufacturer’s value for wavelength? 3 Absorption of Microwaves The object of this part of the experiment is to observe the ability of water to absorb mi- crowaves. Procedure 1.) Adjust the receiver to 180 ◦ and the received 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. Page 5 of 7

Toronto Metropolitan University - PCS213 Distribution, sale or profit without the authorization of the owner of this material is expressly prohibited Report Here is a brief guide for writing the report for the lab. The report should include the following sections: • Title Page – Include: Report Title, Your Name, Course, Section Number, Instructor, TA Name, and Date of Submission. • Introduction – What is the experiment’s objective? • Theory – Derivations of the physics being investigated, or reference to a source that provides a description/equation representing the physics being investigated. – Providing graphs that illustrate or predict how the system under study is expected to behave. • Procedure – Briefly explain the systematic steps taken for the experiment. • Results and Calculation – Tabulate the measurements in an organized manner. – Based on the procedure, one should have a sense of how the tables will look like prior to taking measurements. – Graph the main results. – Provide examples of any calculations. • Discussion and Conclusion – Discuss the main observations and outcomes of the experiment. – Summarize any significant conclusions. Page 7 of 7