Textbook Question
What is the de Broglie wavelength of a 200 g baseball with a speed of 30 m/s?
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32. Electromagnetic Waves
Intro to Electromagnetic (EM) Waves
5:16 minutesProblem 56
Textbook Question
(II) (a) Suppose for a conventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? (b) Suppose, instead, that the X-rays come from a point source (as in Fig. 35–31) that is 15 cm in front of a human body which is 25 cm thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that result.
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Understand the concept of magnification in X-ray imaging: Magnification in X-ray imaging is defined as the ratio of the size of the image on the film to the actual size of the object being imaged. It is influenced by the relative positions of the X-ray source, the object, and the film.
Analyze part (a) - Parallel rays: When the X-ray beam consists of parallel rays, the rays do not converge or diverge. This means that the image size will be the same as the object size. Therefore, the magnification of the image will be 1, indicating no magnification.
Analyze part (b) - Point source X-rays: In this scenario, the X-rays originate from a point source. The magnification will depend on the distances from the source to the object and from the object to the film. The formula to calculate magnification (M) is M = (d + D) / d, where 'd' is the distance from the source to the object and 'D' is the thickness of the object.
Calculate the range of magnifications: Given that the source is 15 cm in front of the body and the body is 25 cm thick, the distance from the source to the film (d + D) will be 15 cm + 25 cm = 40 cm. The magnification will vary across the thickness of the body, with the minimum magnification occurring at the point closest to the source and the maximum at the point farthest from the source.
Discuss the implications: The range of magnifications means that different parts of the body will be imaged at different scales, potentially leading to a distorted image where some parts appear larger relative to others. This effect needs to be considered when interpreting the X-ray images.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Magnification
Magnification refers to the process of enlarging the appearance of an object in an image compared to its actual size. In the context of X-ray imaging, magnification can be influenced by the distance between the X-ray source, the object being imaged, and the film. The formula for magnification is typically given as the ratio of the image distance to the object distance, which helps determine how much larger the image appears compared to the original object.
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X-ray Beam Geometry
X-ray beam geometry describes the arrangement and behavior of X-ray rays as they interact with objects. In the case of parallel rays, the geometry simplifies calculations of magnification since the rays do not diverge. Conversely, when X-rays originate from a point source, the rays diverge, leading to varying magnifications depending on the distances involved, which complicates the analysis of the resulting image.
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Image Formation in X-ray Imaging
Image formation in X-ray imaging involves the interaction of X-rays with matter, where denser tissues absorb more X-rays, resulting in varying levels of exposure on the film. The thickness of the object and the positioning of the X-ray source and film play crucial roles in determining the quality and magnification of the image. Understanding these factors is essential for analyzing how different configurations affect the final image produced.
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