Index Definition and 796 Threads

Hello everyone, Recently I started to use index notation, but still the division is not clear for me. I'll mention just some simple examples that I'm not sure about: Does a =\frac{1}{b_i} mean that a = \sum_{i=1}^{3}\frac{1}{b_i} or a = 1 / \sum_{i = 1}^{3}b_i ? Similarly, does a_i...

Homework Statement http://imgur.com/gTapO Homework Equations The Attempt at a Solution The first one is easy, just use the fact that δi = δ/δxi and it reduces to the sum from with i=1,2,3 of δxi/δxi = 1 + 1 + 1 I tried to do a similar thing with the second one, also using...

Hi, Got a problem with the following derivation: Coming from the Helmholtz equation one gets: \textbf{n}^2=\muc^{2}(\epsilon+i\frac{\sigma}{\omega}) which is of course something like: \textbf{n}=n+i\kappa My question is, how do you obtain the following relations...

I'm not sure if this is the correct place to ask this question, so please let me know if there is a better place for me to post it. I'm having trouble understanding index notation. I understand the basics, such as in the following examples: (a x b) = εijkajbk εijkεiab = δjaδkbδjbδka...

1. A particular fish tank filled with fresh water (n = 1.33) has a coral reef sticker stuck to the exterior wall outside the fish tank. The tank's walls are 2 cm thick, but a goldfish inside the tank sees the sticker 0.6 cm away from the water-wall interface. What is the index of refraction of...

Homework Statement I'm learning QFT and trying to do a basic problem finding the equations of motion from the Euler-Lagrange equation given a lagrangian. The lagrangian is in terms of: F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} so then my issue comes in with this part of the...

Homework Statement I'm reading through the introductory pages of my real analysis book and for some reason I can't wrap my head around this seemingly simple concept. The book is talking about collections of sets and something new to me called the "index set". I apologize ahead of time...

Homework Statement The interference pattern formed is given by I(θ)=4I0cos2(∏dsin(θ)/λ). For d=1×10-5m and λ=500nm plot the intensity pattern as a function of θ for small θ. How would this change if a block of material of thickness 500nm and refractive index n=1.5 were placed over one slit...

My friend gave me a question as a challenge. The question is: Let $G$ be a non-complete simple graph. Prove that $\chi (G) \leq \chi (L(G))$. Here $L(G)$ is the line graph of $G$ and $\chi (G)$ represents the chromatic number of $G$ and $\chi (L(G))$ is the chromatic number of $L(G)$ a.k.a...

Homework Statement Folks Evaluate ##B_{11}## given ##\displaystyle B_{ij}=\int_0^1 (1+x) \frac{d \phi_i}{dx} \frac{ d\phi_j}{dx} dx## where ##\phi_i= sin i \pi x## and ##\phi_j=sin j \pi x## Homework Equations The Attempt at a Solution I calculate ##\displaystyle B_{ij}=\int_0^1...

Hi All, I need to calculate the index time of the following: Max Velocity = 2700mm/s Accel = 4000mm/s/s Decel = 4000mm/s/s Index Distance = x What Equations do I need to utilize in order to calculate the total index time for a specified distance?

Hi, I'm working through a paper and I am quite stupid so some things that maybe obvious are not obvious to me. Say you have some have some complex analytic function that is defined on some simply closed curve, and the index of this function defined on this curve is zero, \int_C...

Homework Statement I am making a very, very simple program that takes in the date (of type string) from the user in the form DD/MM/YYYY. It then confirms whether or not the date is legitimate or not. For example, 09/07/2012 is valid, but 09/17/2012 is not valid. My program compiles...

I was studying Rayleigh Scattering. The theory says that Rayleigh Scattering is approximated to x<<1 where x=(2*pi*r)/lambda where r is the radius of the particle scattering light and lambda is relative scattering wavelength of light. lambda = wavelength of light / refractive index of...

Dear All, thank you for taking the time to view my post. I am a Biologist and I have come across a curious characteristic of proteins that are structural constituents of Nerve cell sheaths (These proteins in addition to lipids surround nerve axons). In general, they seem to have a high...

Homework Statement I'm trying to grasp how the indices are listed when writing out multiple vector products or divergences or gradients, etc. I'm working with 'An Introduction to General Relativity' by Hughston and Tod.Homework Equations A\wedge B = \varepsilon_{ijk}A_{j}B_{k} [A,B,C] =...

Not sure if one exists but can anyone point me in the right direction? Looking for a formula which includes the temperature and partial/total pressure dependencies? I'm trying to find the trajectory of a photon through a cloud of varying (but known) temperature, pressure and humidity. If...

I have my introductory physics students determine the index of refraction of various solids using fairly conventional methods (lining up pins or determining critical angle). I think this experiment would be more interesting if I could vary it more. I would like to find a substance with the...

show that H is subgroup of finite index in Z^n exactly when H is free comutative group of rank n

Homework Statement If I am given a regular, single dimensional array in Java, how do I search for an element in it, and then how do I get the index of that element? I have been trying: int largest; //some number that has been predetermined in earlier code int index3 =...

Hey all, I'm trying to solve a problem in which I have a uniaxial (uniform in two directions, different in the other) crystal with the optical axis normal to the plane of reflection. I call the permittivity parallel to the optical axis ε_par and the permittivity in the other two directions...

Hello world, Index notation is driving me crazy: why on Earth is ∂_i 1/r = -x_i/r^3 ? I would expect it to be -x_i/r^2... Thanks for commenting

In electricity and magnetism, we typically assume that the relative permittivity (or dielectric constant) ε of air is equal to the "permittivity of free space" ε0, and likewise we assume that air has a relative permeability μ equal to the "permeability of free space" μ0. This is equivalent to...

First of all, I'd like to say hi to all the peole here on the forum! Now to my question: When reading some general relativity articles, I came upon this strange notation: T^{a}_{b} = C(dt)^{a}(∂_{t})_{b} + D(∂_{t})^{a}(dt)_{b}. Can someone please explain to me what this means? Clearly...

Can the group refractive index ng be 1>ng>0 ?

or is it possible to create a material with very high refractive index(order of 100's or more)

For a wave traveling from a medium with refractive index n1 to n2 with n2 > n1, the amplitude reflection coefficient is given by: r = (n2 - n1)/(n2 + n1) Consider a beam of light passing through a single pane of glass. There is a reflection at the front surface of the pane, with the...

I'm going through the Light & Optics chapter of Kaplan MCAT prep material & am having a hard time conceptually understanding the relationship between index of refraction & wavelength or with frequency. It says in the book that n = c/v, & "when the speed of the light wave varies with...

I'm reading a few textbooks (Straumann, Schutz, Hartle) on GR and am a little confused working through a small part of each on linearized GR. 1. Relevant equations Using Straumann, the Ricci tensor is given by R_{\mu\nu} = \partial_{\lambda} \Gamma^{\lambda}_{\phantom{k}\nu\mu} -...

I would like to ask if somebody can verify the solution I wrote up to an exercise in my book. It's kind of long, but I have no one else to check it for me :) Homework Statement If H is a maximal proper subgroup of a finite solvable group G, then [G:H] is a prime power.Homework Equations Lemma...

Homework Statement Given the fact that z is one of the n-th roots of unity, find the sum below: 1 + 2z + 3z2 + ... + nzn-1Homework Equations (1-x)(1+x+...+xn-1) = 1 - xn The Attempt at a Solution honestly I don't know how to do this. any help is appreciated

Hi Folks, After a general search online, I have not yet found a simple description of refraction in a medium with an inhomogeneous refractive index. For example: if we have a block of glass with a beam of light shining through it, and the block has a gradient in the real part of the...

Dear Folks: Is there a general method to find all subgroups in a given abstract group?? Many Thanks! This question came into my classmates' mind when he wants to find a 2 sheet covering of the Klein Bottle. This question is equivalent to find a subgroup of index 2 in Z free product...

Hi all, I am thinking about the refractive index, if I have two components with refractive index n1 and n2, respectively, then I mix them up (chemical reactions might happen after the mixing), and should I expect a mixture with refractive index:n=a*n1 + b*n2, where a+b=1. In other words...

Homework Statement At a wavelength of 400nm, the semiconductor ZnSe has a complex refractive index n= 3.0+0.32i A) If 400nm is incidient from air onto ZnSe with θ=tan-1(NR) = 71.6°, What is the refraction angle of the transmitted wave? B) Calculate the magnitude R and phase shift ψ...

How can i calculate the refractive index knowing only the frequency of the light entering the medium from air? n(refractive index) = (speed of light in vacuum) / (speed of light in medium)

How do I show that Maslov index satisfies the next property (product property). Let \Lambda : \mathbb{R} / \mathbb{Z} \rightarrow \mathcal{L}(n), and \Psi : \mathbb{R}/\mathbb{Z} \rightarrow Sp(2n) be two loops, then if \mu is defined as the Maslov index then \mu(\Psi \Lambda )=...

Homework Statement Consider a 2-dimensional line element: ds^2=x^2dx+2dxdy-dy^2 Raise and lower the indices of given vectors by finding the raised index metric, etc, blah blahHomework Equations V_a = (1,-1) and W^a = (0,1)The Attempt at a Solution Solution is given and I understand how to...

Question: A Fsherman sees a Fish in a river at an apparent depth below the surface of the water of 0.75 m. Given that the refractive index of water is 1.33, is the true depth of the Fish below the water's surface: A 0.75 m? B Less than 0.75 m? C 1 m? D More than 1 m? My proposal...

Here is what I've done so far How do I draw the Phase portrait for this system? Have I done everything correct so far? Thanks

Hi all, I'm looking for an equation which will give me the focal length of a biconvex lens given that we know both Radii of curvature, the thickness of the lens and the refractive index inside and outside. An equation is given on wikipedia here http://en.wikipedia.org/wiki/Focal_length as I...

Homework Statement Prove that if p is a prime and G is a group of order p^a for some a in Z+, then every subgroup of index p is normal in G. Homework Equations We know the order of H is p^(a-1). H is a maximal subgroup, if that matters. The Attempt at a Solution Suppose H≤G and...

Homework Statement Hey guys, new to the forums so hopefully you can help. I have been given the frequency (and hence the wavelength) of a microwave of 10GHz, and the conductivity of Al which is 3.53x10^7 Siemens/m. From this I have worked out the skin depth. But it asks also what the...

Homework Statement Prove: If H is a subgroup with finite index in G Then there is a normal subgroup K of G such that K is a subgroup of H and K has index less than n! in G. Homework Equations Note: |G:H| represents the index of H in G |G:H| is the number of left cosets of H in G, ie...

we can calculate the refractive index of liquids like water using a converging lens and mirror by the standard method . r.index of water is less than that of lens(glass) . now taking mercury, whose r.index is > glass, can we do the same experiment and find its r.index ? i believe the answer...

Homework Statement "Calculate the reflection loss when a beam of radiant energy passes through an empty quartz cell assuming the refractive index of quartz is 1.55"Homework Equations I/I_i = ((n2-n1) / (n2+n1))^2The Attempt at a SolutionI'm taking the refractive index through the empty cell...

I recently came across the representation of n(ω) for refractive indices. I also scouted the internet for explanations but could find none, except one on 'complex refractive index' but I don't think that's quite it. So how exactly is refractive index a function of frequency?

Homework Statement do you notice a relationship between the plane and directions of the same miller index? what is it? Homework Equations I've done planes and directions (111), [111], (112), and [112] The Attempt at a Solution I believe the direction is normal to the plane on first...

This isn't strictly a homework problem but anyway... I'm reading through a QFT textbook that is using index notation, and sometimes a new index symbol will be introduced during some mathematics and it always throws me off. I'll give a simple example, take the Minkowski metric: g^{\mu\nu} =...

Why the referactive index of D2O(deutrium oxide) is smaller than H20(water)?As D2O is more denser than H2O.