This is the course content for a waves and optics course that I am currently taking: Oscillations: Review of simple harmonic motion and damped oscillations, coupled oscillators and normal modes.(4) Waves: wave equation, superposition of waves with same and different frequency, Lissajous figures, standing waves, dispersion relations and group velocity.(4) Maxwell's equations: Wave equation, plane, spherical, cylindrical and beam like solutions of the wave equation.(3) Boundary conditions: reflection and transmission at the boundary.(2) Propagation of light in anisotropic media.(2) Coherence: Spatial and temporal.(2) Polarization and double refraction, quarter and half wave plates.(2) Geometrical optics: Paraxial approximation, lens aberrations, ray matrix approach to Gaussian optics, optical systems and resolving power.(8) Interference: Division of wavefront (Young's double slit) and amplitudes (Newton's rings, Michelson interferometer), multi-wave interference-Fabry-Perot interferometer, thin optical coatings (single and multilayer), interference filters.(6) Diffraction: Huygen-Fresnel and Kirchhoff's theories.(2) Fresnel diffraction: rectangular, circular and zone plates.(2) Fraunhoffer diffraction: Slits (single, double) and grating and circular aperture.(2) Introduction to metamaterials.(1) Due to Covid-19, this semester was botched up and the instructor managed to teach only a fraction of the course. I am currently using Vibrations and Waves by AP French and Griffiths for the waves section. I am looking for textbook recommendations for the other topics in the above list. If possible, please mention the topic which is present in each book.
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Every once in a while, we get a question asking for a book or other educational reference on a particular topic at a particular level. This is a meta-question that collects all those links together. If you're looking for book recommendations, this is probably the place to start.  All the questions linked below, as well as others which deal with more specialized books, can be found under the tag  (formerly ).  If you have a question to add, please edit it in. However, make sure of a few things first:   The question should be tagged  It should be of the form "What are good books to learn/study [subject] at [level]?" It shouldn't duplicate a topic and level that's already on the list   Related Meta:
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Edit:  Ok, user  made comment that truly helps narrow the focus of my question. Basically, I'm asking for a self-study course of Mathematical Methods.  Thanks to his recommendation I identified a book that is very close to the answer:  Mathematical Methods in the Physical Sciences by Mary L. Boas  Supposedly, the book covers most of the Math a person needs to learn in order to understand the simulations I presented.  Does this book suit my needs?    Hello,  I have always been interested on the idea to study Math at an Undergraduate level to be able to implement simulations like the followings:  Finite Difference Simulation of the Wave Equation    Heat Equation in Two Dimensions    Besides my precollege experience in Math, I have only been able to do very simple simulations due to my lack of knowledge of Advanced Math. Every time I ask about the inner workings of the simulations I get redirected to papers that look like foreign language to me and, unfortunately, I depend on easy-to-read tutorials to understand them, and while I have found   I'm more interested in reaching the solution myself.  I checked some of the questions related to book recommendations for self-study and while they are very helpful I'm interested in learning by example (There is a book called: "Accelerated C++ Practical Programming by Example" that fits very well my study habits)  Thanks in advance.
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So I am an undergraduate in Electrical Engineering. We had a course on Physics in our freshman year which is equivalent to Classical Mechanics I as taught in MIT. I am interested in studying advanced classical mechanics (which includes Lagrangian formulation and other stuff) as equivalent to Classical Mechanics lecture by Susskind. I wanted to know are they any prerequisites which I should know about before taking this course.   In general what are the prereqs for this course?
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I am taking a course in Mathematical Methods for physicsPhysics (Junior Level).   We are working from   > Mathematical Methods for physicists, George B.Arfken .    I just need online resources covering ( Matrices, Determinants, Vector Analysis, Tensors and differential forms and Vector spaces...etc) to study and understand from.
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I am looking for books about the physics of DSLR, including modern photography optics and sensor electronics. If I already have some books on optics and electronics, I have found fairly hard to find good resource for these fields taking photography as a basis, with examples taken from photography and chapters dedicated to lenses optics for instance.  So far what I have found is either too generic, or, if dealing with photography, lacks the physical expertise I would like to get (I mean books with equations. Everybody loves them.)  Good books for physics of photography exist, but they are quite old, the last good I have found were written by Kingslake in the 70s and definitely miss the non-optical part, and the optical stuff is a bit old-fashioned now (but very nice books BTW).  To sum up, I would like:   Very technical references Dealing with physical issues specific to DSLRs and modern photography, such as diffraction limits, image stabilization, properties of coatings, noise correction - whatever you can think of actually...     EDIT: Based on the first results and a quick glimpse at the references given, I would recommend:   The  looks like a bible. Everything seems to be included. It could be a bit more technical, but it gives a lot of bibliography to go deeper if necessary. , for lighting  and  for sensor technology  and the somewhat easier  for optics   Not to forget the , wonderful resource.
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I'm currently referring to the wave equation derivation given in "Introduction to Electrodynamics" by David J. Griffiths. It follows something like this:  The electromagnetic wave equations are given by the equations: \begin{equation}  v^2_{ph}\nabla^2\textbf{E} = \frac{\partial^2 \textbf{E}}{\partial t^2} \tag{1}\label{eq1} \end{equation} \begin{equation} v^2_{ph}\nabla^2\textbf{B} = \frac{\partial^2 \textbf{B}}{\partial t^2} \tag{2}\label{eq2} \end{equation} Where, $v_{ph} = \frac{1}{\sqrt{\mu\epsilon}} $, is the velocity at which the wave travels in the medium    We have the Heaviside' form of Maxwell's equations in differential form, $$\nabla . \textbf{E} = \frac{\rho}{\epsilon_0}$$ $$\nabla . \textbf{B} = 0$$ $$\nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t}$$ $$\nabla \times \textbf{B} = \mu_0 \left(\textbf{J} + \epsilon_0\frac{\partial\textbf{E}}{\partial t}\right)$$ In a vacuum and charge-free space ($\rho = 0, \textbf{J} = 0$), these equations are:, \begin{equation} \nabla . \textbf{E} = 0 \tag{3}\label{eq3} \end{equation} \begin{equation} \nabla . \textbf{B} = 0 \tag{4}\label{eq4} \end{equation} \begin{equation} \nabla \times \textbf{E} = -\frac{\partial\textbf{B}}{\partial t} \tag{5}\label{eq5} \end{equation} \begin{equation} \nabla \times \textbf{B} = \mu_0\epsilon_0\frac{\partial\textbf{E}}{\partial t} \tag{6}\label{eq6} \end{equation} We also have the vector identity for any vector function of space, \begin{equation}  \nabla \times \textbf{V} = \nabla.(\nabla\textbf{V}) - \nabla^2\textbf{V} \tag{7}\label{eq7} \end{equation} We thus try to find the curl of $ (5) $ \begin{equation} \nabla \times (\nabla \times \textbf{E}) = \nabla \times -\frac{\partial\textbf{B}}{\partial t} = -\frac{\partial}{\partial t}(\nabla \times \textbf{B}) \tag{8}\label{eq8} \end{equation} Plugging $(6)$ into $(8)$, we get \begin{equation} \nabla \times (\nabla \times \textbf{E}) = -\frac{\partial}{\partial t}\left(\mu_0\epsilon_0\frac{\partial\textbf{E}}{\partial t}\right) = -\mu_0\epsilon_0\frac{\partial^2\textbf{E}}{\partial t^2} \tag{9}\label{eq9} \end{equation} Using the identity (7), \begin{equation} \nabla.(\nabla\textbf{E}) - \nabla^2\textbf{E} = -\mu_0\epsilon_0\frac{\partial^2\textbf{E}}{\partial t^2} \tag{10}\label{eq10} \end{equation} Plugging (3) into (10), we get \begin{equation} 0 - \nabla^2\textbf{E} = -\mu_0\epsilon_0\frac{\partial^2\textbf{E}}{\partial t^2} \tag{11}\label{eq11} \end{equation} With a slight bit of rearrangement we can see that, $$- \nabla^2\textbf{E} = -\mu_0\epsilon_0\frac{\partial^2\textbf{E}}{\partial t^2} $$ $$\nabla^2\textbf{E} = \mu_0\epsilon_0\frac{\partial^2\textbf{E}}{\partial t^2}$$ \begin{equation}  \frac{1}{\mu_0\epsilon_0}\nabla^2\textbf{E} = \frac{\partial^2\textbf{E}}{\partial t^2} \tag{12}\label{eq12} \end{equation} (12) and (1) correspond to the same equation under the conditions imposed. Following a similar line of reasoning for equation (6), we will get the equation; \begin{equation}   \frac{1}{\mu_0\epsilon_0}\nabla^2\textbf{B} = \frac{\partial^2\textbf{B}}{\partial t^2} \tag{13}\label{eq13} \end{equation} which corresponds to equation $(2)$. Thus, we have obtained the electromagnetic wave equation from Heaviside' form of Maxwell's equations in differential form.   Is there a way to derive the same wave equations without assuming to be in a vacuum and charge-free space i.e $ \ \textbf{J} = 0, \rho = 0$?
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This is about a step in a derivation of the expression for the relativistic Doppler effect.  Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is emitted at frequency $f_s$ and wavelength $\lambda_s$. The frequency $f_0$ and wavelength $\lambda_0$ received by the observer will be different.  Some textbooks now argue that the wavelength received by the observer is given by $\lambda_0=(c+u)T_0$, where $T_0$ is the time period of the wave in the observers frame. The argument given is that the successive "crests" will be an extra distance $uT_0$ apart due to movement of the source. Upon relativistically transforming the time period in the source frame to the observer frame, the correct result $f_0=f_s\sqrt{\frac{c-u}{c+u}}$ is obtained.  But the argument for the wavelength seems reminiscent of the classical Doppler effect for sound. Is it really applicable here through this argument? And is there a way to show the same result for $\lambda_0$ mathematically?
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What textbook would you recommend for a bachelor in theoretical physics to study ? I don't want to focus too much on chaos, just having a broad view of every interesting characteristic is enough. Physical meaning behinds equations should be explained.  Some related resources:   , but obviously those are math-y.  While there are some overlaps, the evolution of a simple oscillator can evoke interesting dynamics characteristics. , but I'm not sure if studying only fluid dynamics is too narrow for me.
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How can I derive the ? I don't want to use hyperbolic functions and the fact that the light waves travel by forming spherical wavefronts. Is there a way to derive the Lorentz transformations applying the conditions I have mentioned. I was unable to understand the method given in Landau and lifshitz deeply. That's why I want a method other than the one using hyperbolic functions
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I was studying a  problem where optical light with a wavelength of 500&nbsp;nm travels through a gas with refractive index $n$.  If we look at the equations for wave motion and index of refraction  $$c=\lambda_0\nu\quad\text{(in vacuum)}$$  $$v = \lambda\nu\quad\text{(in medium)}$$  $$n = c/v$$  we see that, if the frequency is constant, the wavelength decreases in the medium compared to vacuum. Is this a consistent property at all frequencies and for all mediums with refractive index real and greater than 1?  Are there dielectrics which change the frequency (still for n > 1), and is there an example of that?
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For some reason I don't understand, Google Scholar thinks two of my papers are the same, despite different titles, co-authors, and publication years. When I click on one ("Resonant absorption as mode conversion?") it lists 27 versions, most of which are the completely different paper ("Three Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I"). It therefore combines the citations for the two. How can I split them? I even tried deleting both papers and adding them manually from scratch, but without success.
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Can someone explain why a longitude wave can pass through the liquid, but a transverse wave can't. And can someone recommend some good animation of these processes.
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How is the following classical optics phenomenon explained in quantum electrodynamics?   Reflection and Refraction   Are they simply due to photons being absorbed and re-emitted? How do we get to Snell's law, for example, in that case?  Split by request: See the other part of this question .
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Can anyone recommend some good textbooks for undergraduate level computational physics course? I am using numerical recipe but find it not a very good textbook.
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How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics.  I need an clear argument that   involves the equations of motion for just the potentials $A^0$ and $\mathbf{A}$, and not the electric and magnetic fields.   includes sources $\rho$ and $\mathbf{J}$ in the equations of motion.  This is to justify the assertion that there are degrees of freedom that decouple from the rest of system. does not critically rely on quantum field theoretic arguments (although any supplementary remarks are welcome).     To illustrate the level of clarity I expect, I provide an argument in the Coulomb gauge $\nabla\cdot \mathbf{A} = 0$:  Of the four field degrees of freedom, the gauge condition $\nabla\cdot \mathbf{A} = 0$ removes one degree of freedom (the longitudinally polarized EM waves).  To show that among the remaining three degrees of freedom only two are propagating, consider the field equations of motion in the Coulomb gauge:  \begin{align} \nabla^2 A^0 &amp;= -\rho/\epsilon_0,\\ \big[\frac{1}{c^2}\frac{\partial^2}{\partial t^2}-\nabla^2\big]\mathbf{A}&amp;= \mu_0 \mathbf{J}-\nabla \frac{1}{c^2}\frac{\partial}{\partial t}A^0. \end{align}  The first equation is NOT a wave equation for $A^0$, and thus does not propagate.  The final equation IS a wave equation, and describes the propagation of two degrees of freedom (Gauss' law in first eq. can be solved, and then inserted into the second equation to show that $\mathbf{A}$ only couples to the Solenoidal part of the current).
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Assume I want to learn math and physics enough to reach a level where I understand Maxwell's equations (The terms and reasoning in the equations I.e. why they "work"). What would I have to learn in order to have the tools I need to make sense out of it?  I'm kindof looking for a road map which I can use to get started and know what to focus on. The fields are pretty big so some pruning would be very helpful (if possible)
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The  is a well-known and very useful tool for solving problems in electrostatics.  Unfortunately, when I was taught this method, it was presented simply as an algorithm. No real physical justification was given for its usage, and there was a complete absence of rigorous mathematics. The method has always been a little hazy to me since.  If someone could give a rigorous first-principles derivation of this method from Maxwell's equations (perhaps simply Coulomb's law?), it would be most appreciated.