Index Definition and 795 Threads

Hello everyone! I'm trying to learn the derivation the covariant derivative for a covector, but I can't seem to find it. I am trying to derive this: \nabla_{α} V_{μ} = \partial_{α} V_{μ} - \Gamma^{β}_{αμ} V_{β} If this is a definition, I want to know why it works with the definition...

Hey everyone, I'm struggling with the summation notation for matrices and vector operations, multiplication in particular. Please refer to the image below where I've typed it all out in Word, its too cumbersome here and I want my meaning to be clear...

hi gang, just a quick clarification please :) was looking at the Wiki articke on Frequency modulation http://en.wikipedia.org/wiki/Frequency_modulation This comment is in the Modulation Index section... The signal frequency is referring to the applied audio signal doing the...

The light travel by it's in a straight line in vacuum, but when we see through the glass the glass has a refractive index which slows down the speed of light so when I see through the glass I don't see the actual distance. Moreover, the gases particles has refractive index and slows down the...

In optics, given the below formula nλ= A + B/λ2 + C/λ4 +... where A, B and C are constants. From the above relationship we can deduce that as the wavelength λ increases, the variation of refractive index nλ decreases. How do we measure the constant value of A,B and C at the first...

hello, Do I have the right to perform the following : gjo,i + g0i,j = (gj0 δij + g0i ),j = (2 g0i ),j Thank you, Clear skies,

Homework Statement See image Homework Equations n1sin(theta1) = n2sin(theta2) 1/s + 1/s' = 1/f The Attempt at a Solution My question is for the second part. I think I've figured out why I got it wrong, but I'm not sure. So since the object distance (s) should be approximately 21 cm, then...

When a light wave of the form E=E0eiω hits the surface of a metal, the refractive index if given(considering restoring force of metal atoms and damping equal to 0), by n2=1-p2/ω2 where p=plasma frequency and ω= frequency of the wave. In the case where n2<0, n is complex. and hence the light wave...

Hi, I have to make the classic egg drop contraption but we're only allowed to use plastic drinking straws, index cards, and hot glue. the width also has to be smaller than 4x4 inches but it can be as tall as we want it to be (but preferably small) and it has to have a door of some sort...

Homework Statement Show that the following can be expressed as a quadratic equation 2^{x}-1 = \frac{2}{2^{x}}Homework Equations Show that the quadratic has only one real solution at x = 1 The Attempt at a Solution Well, my biggest problem is the main part of the task, converting the equation...

Homework Statement Simplify; expressing with positive indices. \frac{x^{-2} - y^{-2}}{x^{-1} - y^{-1}} The Attempt at a Solution Hello, I'm doing first year uni math and over the holidays, I forgotten my index laws and as a result I'm stuck on this question :rolleyes: I know that...

Homework Statement I have to design an experiment to determine the difference in refractive indices for different colors. Assume you have : color filters,glass block Homework Equations The Attempt at a Solution I want to do it buy shining a white laser light through...

I see summation examples in my textbooks often give something where there is an ai next to the summation itself. It also shows the index of notation to be i=m at the bottom an m at the top with the whole thing equal to am+am+1+...+an-1+an What mathematical representation are they trying to...

Hello! I have a question concerning the relation of the index of refraction of a material with E/M wave frequency. If we take the classical Feynman approach, we can envision the material as a series of atoms, with electrons bound with springs to the nuclei. Let the natural frequencies of...

Homework Statement A beam of light travels through air (n= 1.0003) and strikes an unknown material at an angle of 50.0 degrees. The new angle of refraction is 25.0 degrees. What is the index of refraction of this material? Homework Equations sin\theta2 / sin\theta1 = n1/n2 The...

Homework Statement A non-expanding/non-contracting laser beam having a diameter 0.132 m in air strikes a piece of glass (ng = 1.62) at an angle of 52°. What is the diameter of the beam, in m, in the glass? Homework Equations snell's law, n1sin(θ1)=n2sin(θ2) The Attempt at a...

Most textbooks list the real part of the index of refraction. How would I go about calculating the imaginary part of the index of refraction of air?

Homework Statement We know, for constant n, \frac{\partial L}{\partial y} = \frac{d}{dx} (\frac{\partial L}{\partial y'}), where we define L as being the optical light path length, and y' is the derivative of y with respect to x, and L = L(y, y') = n \sqrt{1 + y' ^{2}}. However...

given the vector in the first equation below, does that necessarily imply the third equation, as shown? {{u}_{a}}{{e}^{a}}={{x}_{a}}{{e}^{a}} {{u}_{a}}{{e}^{l}}g_{l}^{a}={{x}_{a}}{{e}^{l}}g_{l}^{a} {{u}_{a}}{{e}^{l}}={{x}_{a}}{{e}^{l}}

Hi, can anyone help me out with the refractive index of pure gold at microwave freguencies? (Specifically something close to 2.4 GHz, or your average household microwave oven) Much obliged!

Homework Statement There is a diagram in the problem statement so here is a link to the image of the problem: http://imgur.com/KDrRsyO Homework Equations Snell's Law: n_{1} * sin(\theta_{1}) = n_{2} * sin(\theta_{2}) The Attempt at a Solution My attempt using Snell's law...

Hi, I've been wondering about this forever and I finally decided to ask on the forums. In relativistic index notation (with c= \hbar =1) with the minkowski metric g\mu\nu=diag(1,-1,-1,-1), the 4-vector x^{\mu}=(t,x,y,z)=(x^0,\vec{x}), and with the del operator defined as \partial_{\mu}\equiv...

Homework Statement The problem is page 5 on: http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/Paper3_2010_.pdf I will just summarise the question: The refractive index of space,n, at a distance r from the sun is given by √(1+5920/r). The light from a distant star is deflected by a...

hi all...i have problem in understanding in array index. my codes are as below subroutine tmz2d implicit none double precision :: phi double precision :: cosphi,sinphi double precision :: d,dp,dpp,d1,d2 integer...

Refractive index = {speed of light in vacuum}/[speed of light in the medium] This value also equals the ratio{sin i/ sin r} Is there any mathematical proof showing that {sin i/ sin r}= {speed of light in vacuum}/[speed of light in the medium]

Hi, I have to write a "thesis" (short paper using only calculus and no philosophical concepts) about a very big and ambiguous concept, and I was hoping some of you could point me in the right direction. It says... "We can assume that at any moment every location in the universe observes...

What is the physical significance of Refractive Index(RI) ?

Homework Statement A prism of 90-45-45 was placed between a microwave receiver and transmitter. What steps should I take to know the index of refraction of the prism given that its material is not transparent to microwave? I positioned the prism so that a side of the prism is perpendicular to...

Homework Statement Two optically flat glass plates, 16.0 cm long, are in contact at one end and separated by 0.0200 mm at the other end. The space between the plates is occupied by oil with index of refraction 1.45. The index of refraction of the glass plates is 1.55. The plates are...

ElectroMagnetic Wave In Liquid.. Help with Index of Refraction?? Homework Statement Consider the propagation of an electromagnetic wave in some liquid. The y-component of its electric field is given by Ey(x,t)=4.3 x104 V/m sin(5.40E-2m-1x + 6.00E+0 x106 s-1 t). How large is the index of...

How can I show that a first-degree Besselfunction a la Jn=Bessel(n,eta) for large etas always lead to something like a bathtub? I.e. how can I show that J(n=eta) produces sth like a overshoot? I would really appreciate every idea.

Newtons Rings Calculations - Values Not Working Out I'm having trouble with a Newtons Rings experiment to determine the refractive index of water. I'm using a sodium light source and a Vernier scale traveling microscope to measure the radius of the bright circles (I don't know if measuring the...

Hi, I am running a code in MATLAB process 8 columns and over 500 rows of data but i get the above error. With 6 columns, the code works well. Your help is important.

Imagine I have a set of discrete points equally spaced out and indexed from 1 to n (a 1D grid). On a cartesian grid if the spacing, dx, is constant the index can be obtained simply by: i = floor(x/dx) That was pretty simple, now if the cartesian grid is stretched (i.e. dx is not constant)...

Homework Statement What is the minimum thickness of coating which should be placed on a lens in order to minimize reflection of 401 nm light? The index of refraction of the coating material is 1.31 and the index of the glass is 1.56. Homework Equations I haven't been able to attempt the...

Homework Statement Simplify the following, where A and B are arbitrary vector fields: f(x) = ∇\bullet[A \times (∇ \times B)] - (∇ \times A)\bullet(∇ \times B) + (A \bullet ∇)(∇ \bullet B) I know that the correct solution is A \bullet ∇2B, according to my professor. However, I can't...

Homework Statement For my lab I beamed a laser through an equilateral triangular prism. The angle of incidence was 13 degrees. The light left the prism at an angle 15 degrees to the normal. How would I calculate the index of refraction of the prism? (air = 1) Homework Equations The...

Imagine a dielectric made of of alternating layers of widths A and B and refractive indices (a*) and (b*). Find the effective refractive index, N So in general: c/n = wavelength x frequency = phase speed My thinking was find the total time taken for the wave to propagate through the...

Is there a proof that ∏(√n) increments only when n is a centered polygonal number with a prime index? ∏(n) is the prime counting function n=p^2-p+1 for a prime p 3, 7, 21, 43, 111, 157, 273, 343, 507, 813, 931, 1333... http://oeis.org/A119959

Homework Statement consider the position vector expressed in terms of its cartesian components, r=xiei. Let w=wjej be a fixed vector whose components wj are constants that do not depend on the xi, so that δwj/δxi = 0 Homework Equations I am trying to evaluate ∇((wXr)^2) The...

Hello,, I try to convert a fortran program to matlab. I want to make an absorbing boundary model. But when I run it, I keep getting an error says: ? Attempted to access w(12); index out of bounds because numel(w)=11. Error in ==> absorb_bound_coba at 45...

Hi, I have read on a website that the refractive index of glass is related to the number of electrons it has per unit volume. I don't recall which website it was, but is it true? & if so what is the quantitative description behind it? or is it a lot more complicated :) Many thanks for...

What is the refractive index for silicon ?

Just an idea: is there an index theorem for an n-dimensional Hamiltonian H = -\triangle^{(n)} + V(x) which "counts" the bound states (H - E) \,u_E(x) = 0 i.e. eigenfunctions and eigenvalues in the discrete spectrum of H?

When I read A.Zee's QFT in a Nutshell, he asked me to do the calculation of his exercise IV.4.6: (A.Zee called these the Pontryagin Index) Let g(x) be the element of a group G. The 1-form v = gdg† is known as the Cartan-Maurer form. Then tr v^N is trivially closed on an N-dimensional manifold...

Let G be a finite group and let G = H_1 \cup H_2 \cup H_3 . Show that [G: H_i] = 2 for i = 1, 2, 3. There was a hint for this question saying to first prove that at least one of the subgroups has index 2 in G. So far I am not sure how to even start this problem. I know that the orders of...

Homework Statement I need to find the refractive indexes of the core and cladding of an optical fibre by using the specs found here http://www.photonics.byu.edu/FiberOpticConnectors.parts/images/smf28.pdf Then I'm suppose to calculate the Numerical aperture and compare it with the one listed...

(r×∇).(r×∇)=r.∇×(r×∇) now in index notation it is written as, =xi∂jxi∂j-xi∂jxj∂i but when I tried to prove it ,it just came out twice.can anyone tell how it is correct(given is the correct form).i really mean that i was getting four terms which gave twice of above after reshuffling...

Homework Statement ∫ ∂k(gixiεjklxl dV Can anyone make sense of this? I know I'll need to apply the chain rule when taking the derivative, but I'm not quite sure how to proceed. Also, this is part of a larger problem where g is a gravity vector existing purely in the -z direction, but I...

I have seen double sums, but have come across a problem involving sums over primes. However, this sum is inside a second sum, and is taken over all primes that divide the outside index, like this: \sum_{k=1}^{n} \sum_{p | k} \frac 1p for p prime. Is there any way to manipulate this...