Author: Tru Physics
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Chapter 10: The Relativistic Doppler Effect
10.1 Introduction to the Relativistic Doppler Effect The Doppler effect is the change in frequency and wavelength of a wave in relation to an observer who is moving relative to the wave source. In the context of special relativity, the Doppler effect plays an important role in the analysis of the behavior of electromagnetic waves,…
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Chapter 9: The Lorentz Transformations
9.1 Introduction to the Lorentz Transformations The Lorentz transformations are a set of mathematical equations that describe the relationship between the space and time coordinates of events in different inertial frames of reference moving relative to one another. These transformations are essential for understanding the principles of special relativity, including time dilation and length contraction.…
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Chapter 8: Introduction to Special Relativity
8.1 Introduction to Special Relativity Special relativity is a theory developed by Albert Einstein in 1905, which revolutionized our understanding of space and time. This theory was developed to reconcile the principles of classical mechanics with those of electromagnetism, particularly the constant speed of light in a vacuum. Special relativity has important implications for our…
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Chapter 7: X-Ray Diffraction
X-ray diffraction is a powerful technique used to determine the atomic and molecular structure of crystalline materials. By analyzing the interference patterns produced by X-rays scattering off the crystal lattice, we can derive valuable information about the arrangement of atoms within the crystal. This chapter will introduce the basics of X-ray diffraction and its applications.…
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Chapter 6: Multiple-Slit Diffraction
6.1 Introduction Multiple-slit diffraction occurs when light passes through an array of narrow, equally spaced slits, creating an interference pattern of bright and dark regions. In this chapter, we will discuss the basics of multiple-slit diffraction and explore the underlying principles that govern the formation of the resulting patterns. 6.2 Double-Slit Diffraction Double-slit diffraction is…
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Chapter 5: Fresnel and Fraunhofer Diffraction
5.1 Introduction to Diffraction Diffraction is a phenomenon that occurs when light waves encounter an obstacle or an aperture, causing them to bend and spread out. There are two main types of diffraction: Fresnel diffraction and Fraunhofer diffraction. This chapter will discuss the basic principles and differences between these two types of diffraction. 5.2 Fresnel…
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Chapter 4: The Michelson Interferometer
4.1 Introduction to the Michelson Interferometer The Michelson Interferometer is an optical instrument that utilizes interference to measure distances and wavelengths with high precision. It was invented by Albert A. Michelson in the late 19th century and has been used in various scientific experiments, including the famous Michelson-Morley experiment, which tested the existence of the…
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Chapter 3: Interference
3.1 Introduction to Interference Interference is a fundamental phenomenon in wave theory that occurs when two or more waves superpose to form a resultant wave. The principle of superposition states that when two or more waves overlap, the displacement at any point is the vector sum of the displacements of the individual waves. In the…
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Chapter 2: Magnification
2.1 Introduction to Magnification In optics, magnification is the factor by which an object’s size appears larger or smaller than its actual size when viewed through an optical instrument, such as a lens or mirror. Magnification can be expressed as a dimensionless value or as a ratio of the size of the image to the…
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Orthogonality
Introduction In mathematics and physics, orthogonality is a key concept, not just confined to vectors in Euclidean space but also extended to more abstract concepts like functions. Two functions are said to be orthogonal if their inner product is zero. Inner Product of Functions In the context of function spaces, the inner product of two…