Unit 13 Lab - Trisha Menon

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University of Illinois, Urbana Champaign *

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Physics

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Apr 3, 2024

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PHY-222 Classical Physics II (online) Radio Waves & Electromagnetic Fields SIM Homework 1) For this question, use the Radio Waves & Electromagnetic Fields simulation to guide your understanding of how Radio broadcasting and Radio receivers work. a) How is the radiating electric field (or electromagnetic signal) produced when radio stations broadcast? Include a description of what is producing the signal as well as the reasoning behind how this could produce a signal. The electromagnetic radiation is created from the accelerating charges. I could see the electrons in the radio transmitter oscillating and accelerating. This forces the electrons to change their directions because of the oscillation. b) How does your antenna work to detect this electromagnetic signal produced when radio stations broadcast? Include the physics principles that support your description of how this signal is detected. Electromagnetic radiation is a type of energy that constantly exerts an oscillating force on the electrons. The force is exerted in only one direction, but changes this direction to the opposite to produce a rhythmic and cyclical process. The radio waves pass by in the antenna, pushing on the electrons in the antenna and finally making the electrons oscillate for the length of the antenna and produce currents. Therefore, the antenna detected the electromagnetic signals. 2) Using the simulation, adjust the transmitter so that it is in sinusoidal mode and the electrons are oscillating up and down at a regular frequency. This is how radio waves are broadcast. Set it so that both “display the curve” and the “radiated field” boxes are checked. a) What does the curve represent? (Select the correct statement below) i) The line of electrons being sprayed off of the antenna that then cause the receiver electron to move. ii) The path that an electron will follow due to the electromagnetic wave. iii) The evenly spaced electrons moving up and down between the two antennae. The field of negative charges that are moving through space. iv) The strength and direction of the force that would be exerted by the electromagnetic wave on an electron. Correct statement is: _____ iv _____

PHY-222 Classical Physics II (online) b) With the frequency set at the mid-point of the slider and the amplitude set at the mid-point of the slider, approximately how many grid marks is the wavelength of the wave (use the pause button and step button as you need to in order to get a good measure, and round to the nearest whole grid mark)? The wavelength of the transmitter is about 5 grid marks. If the amplitude is increased, the wavelength (Select the correct statement below) i) Decreases ii) Increases iii) Stays the same Correct statement is: ____ iii ______ c) Use the simulation to evaluate the following True/False statements. i) If the oscillation frequency of the transmitting electron decreases, the oscillation frequency of the electron in the receiver is instantaneously affected. Statement is: ___ False _______

PHY-222 Classical Physics II (online) ii) The electron in the receiving antenna oscillates at a lower frequency than the electron in the transmitting antenna because of the distance between the antennas. Statement is: ___ False _______ iii) If the frequency of oscillation increases but the amplitude of the electron oscillation remains the same, then the electron in the transmitting antenna is experiencing larger accelerations (recall what you know about acceleration and motion). Statement is: ___ True _______ Explain your reasoning for your answer. Recall what you know about acceleration and motion and include in your explanation how this affects the strength of the transmitted electromagnetic signal. The electrons are moving faster as they oscillate for the frequency to increase and the amplitude to stay the same. When the electron moves faster toward its peak and then away from the peak at a new frequency, it experiences bigger change in velocity. This means that the time it took for the change to happen is less than that of the old frequency and it indicates the acceleration should be higher. iv) If the amplitude increases but frequency remains the same, the electron at the receiving antenna experiences larger peak forces but oscillates at the same frequency as before. Statement is: ___ True _______ v) If the frequency of the transmitting electron decreases by a factor of two, it will now take longer for the electromagnetic signal to reach the receiving antenna. Statement is: ____ False ______ vi) If the frequency decreases, the wavelength decreases. Statement is: ___ False _______ vii) The electromagnetic waves generated by the transmitting antenna produce currents in the receiving antenna. Statement is: ____ True ______ viii) When the electron in the transmitting antenna is at its peak height, the electron in the receiving antenna is always also at its peak height. Statement is: ____ False ______ d) For the radio wave transmitter in the simulation, which of the following orientations of the receiver antenna will pick up the signal? (Select all that will) i) An antenna oriented vertically ii) An antenna oriented horizontally (parallel to the ground) with one tip pointing towards the transmitting antenna (so it is oriented East-West) iii) An antenna oriented horizontally and perpendicular to the antenna in the previous answer (so it is oriented North-South) Correct statement is: ____ i ______

PHY-222 Classical Physics II (online) e) Which one of the following sets of graphs below of position vs. time, velocity vs. time, and acceleration vs. time corresponds with the motion of the electron in the receiving antenna? (It may help to remember the relationship betw een force and acceleration, and use the “Step” feature to step through the motion of the electron and have the vectors display the “force on an electron”.) • • The correct graph is: ____ iii ______

THIN LENS RAY TRACING By computing the amount of refraction occurring at each surface of a lens, we can determine the precise direction of any given ray when it emerges from the lens. By extending this direction back into the lens until it meets the incident ray's original path, we can construct a plane. This plane is the PRINCIPAL PLANE of the lens. We may trace the paths of all entering rays as if all refraction occurred at this plane. Diagram 2.1: Construction of the principal plane. In thin lens ray tracing, we make two assumptions: 1. the thickness of the lens does not affect the power of the lens; and 2. the lens has the same medium on both sides. We will discuss what happens when these two assumptions are not true in the next lesson. We will draw converging lenses with base in prisms at top and bottom of the principal plane, and diverging lenses with base out prism at top and bottom of the principal plane. Diagram 2.2: Refraction through a converging and a diverging lens. The AXIS is the ray which travels perpendicular to the principal plane, and is therefore not deviated. The OPTICAL CENTER of a lens is the point where the axis crosses the principal plane. We may now state the rules for thin lens ray tracing. CONVERGING LENSES: 1. The light ray traveling parallel to the axis will be refracted at the principal plane, and emerge to travel through the secondary focal point. (f '). 2. The light ray traveling through the primary focal point (f') will be refracted at the principal plane, and emerge parallel to the axis of the lens.

3. The light ray that travels through the optical center of the lens will not be refracted. Diagram 2.3a: Refraction through a converging lens. DIVERGING LENSES: 1. The light ray traveling parallel to the axis will be refracted at the principal plane, and emerges if it had come from the secondary focal point (f'). 2. The light ray traveling toward the primary focal point (f) will be refracted at the principal plane, and emerge parallel to the axis of the lens. 3. The light ray that travels through the optical center of the lens will not be refracted. Diagram 2.3b: Refraction through a diverging lens. There are two items that must be kept in mind. First, the object has rays reflecting from all points on it and going in all directions. We are drawing only the principal ones. Second, these rules are valid only for rays that are traveling "close" to the axis with respect to the focal length of the lens. When the rays come in obliquely and not close to the axis, aberrations are generated which are discussed in the lesson on aberrations. The rules would be true for other rays only if the lens surfaces were parabolic instead of spherical. We will use the convention that object distance is positive if the object is on the incident side of the lens. Image distance is positive if the image is on the refracted side of the lens. Image size and object size are positive if the image or object is above the axis or erect. If the image or object is below the axis or inverted then the image or object size is negative. Object size and distance will always be positive for single lens systems There are examples of virtual objects in a later lesson, when we consider multiple lens systems.

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