Index Definition and 795 Threads

Dear forummers, I'm trying to solve a problem that is displayed in MATLAB below:- ? Attempted to access x(2); index out of bounds because numel(x)=1. Error in ==> fit_fun at 5 Fit_fun_val= x(1)^2 + x(2)^2 + x(3)^2; Error in ==> jack_immune at 47...

Can anyone explain this property of shifting the index on the summation notation? I'm reading a book and came across this which has confused me. I don't see how these are equal: \sum_{k=1}^n \frac{1}{k(k+1)} = \frac{1}{2} + \sum_{k=2}^{n+1} \frac{1}{k(k-1)} It's part of an explanation that...

Hello, Here is my scenario: I am trying to run a code a 100 times, so I use a for loop statement i=1:100. The 1 to 100 stands for 1 to 100 days. Now I want to see how much randomness my results give and so I want to simulate this whole 100 days thing twice. So I think my code would look...

Homework Statement A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 30 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?Homework Equations n=c/v d=rtThe Attempt at a Solution So, I'm having difficulty...

In Introduction to Vector Analysis, § 1.16 Tensor notation, Davis and Snider introduce index notation and the Einstein summation convention, Kronecker's delta and the Levi-Civita symbol. They present the following equation, on which they base some proofs of vector algebra identities...

In Linear Algebra and its Applications, David Griffel writes, "The components of covectors are often denoted by superscripts, rather than subscripts." This differs from the usual convention, doesn't it? Unless I've completely misunderstood the concept (quite possible!), the introductory texts...

I am trying to understand the relation between transparency and refraction index. Searched this forum so found and read some topics too. As I undertand, transparency is related with atomic structure and phonons. This is ok. If light beam (or say photons) faraway from phonons (and atoms), they...

can some one tell me how the refractive index changes with the wave length of the light?

Optics, prism and angle of deviation 1. Angle of incidence, emergence and deviation are respectively 30, 60 and 45 degree. 2. 3. I think that it is irrespective of the refractive index.

Building Materials Refractive Index?? Hi all, does anybody know the refractive indices of these materials (used in houses)? - Wall bricks - Wood (used in doors) - Glass - Plastic - Concrete (in ceiling and floor) and any other common materials :) thanks in advance

in order to reduce unwanted light scattering from a sample, a trick often used is to immerse it in a higher refractive index liquid . This is called index matching. Could anyone elaborate how it reduces unwanted scattering? regards pilo440

I am sure this topic has been discussed a million times so how can once more hurt? I am only just being introduced to physics at school and a question came to mind when I was thinking about a game called "Crysis" in which the main character can become invisible. 'Cloaking' or 'invisibillity'...

Dear all, I'm reading the GR book by Ray D'Inverno. I would like to do some additional exercises about tensors. I can get the Schaum Outline on tensors. Is there any other book or online resource where I can find additional exercises to get more familiar with tensor manipulations? Thanks...

Hey all, The way I was taught GR, the summation convention applies on terms where an index is repeated strictly with one covariant, one contravariant. But reading through a translation of Einstein's GR foundations paper just now it looks like the index placement doesn't matter (I've seen it...

Snell's Law -- figuring out index of refraction Homework Statement A light ray enters a rectangular block of plastic at an angle of θ1 = 45.0° and emerges at an angle of θ2 = 79.0°, as shown in Figure P35.71. (the image is of light entering the block from the west, and exiting from the...

Homework Statement Prove using index notation that, the x denoting a cross-product. (del x f del g)=del f x del g Homework Equations The Attempt at a Solution dif etc. denote partial derivatives. RHS=eijkdjfdkg LHS-I'm not even quite sure how to write it in index...

Question In index notation, can you have more than two occurances of the same index in the same term? Let me provide and example: Let's say I have a two index tensor, M{\alpha \beta}, and I contract it with itself: M_{\alpha \beta} M^{\alpha \beta} Then let's say I wish to operate on...

Say that you want to create an index, to quantify technological level of humanity at any time. This index puts a value on the level of today as good as the level of technological advancement year 1662 or 400 BC. It can be used in predictions of the future and so on.. What factors; quantities...

Homework Statement The index of refraction for violet light in silica flint glass is 1.65 and for red light is 1.62.What is the angle of deviation for the red ray passing through a prism of apex angle 59.7 degrees. If the angle of incidence is 47.4 degrees. Homework Equations nglass...

Homework Statement for i=1: max (size(z)), if real (z(i))>0, z(i)=-2; end end for i=2: max (size(p)), if real (p(i))>0, p(i)=-2; end end Homework Equations why there is always error.. it said that ? Attempted to access z(1); index out of...

Hi, I'm new to this. I've always wished to create an index, for hobby and all. Not the kind of index in lengthy books, but the statistical kind, like a happiness index - http://www.google.com/search?hl=en&q=happiness+index&btnG=Google+Search Those kinds; I don't know if they have a...

I've already posted a couple of index notation questions on here and I've gotten very helpful responses. So I thought I'd try my lucky again, though I'm a little more stumped on this question than I was on the others... Let \vec{x} be the position vector and \vec{r} the radial unit vector. In...

How do I make sense of the index notation expression r_j r_i p_j ? What I really *want* it to be is \vec{r} (\vec{r} \cdot \vec{p}) And it turns into this, as long as I can commute the r_i[/tex] and r_j...right? (By the way, here \vec{r} is just the position vector and...

I'm trying to simplify the expression (\hat{r} \times \vec{\nabla}) \times \hat{r}, where \hat{r} is the radial unit vector, using index notation. I think I'm right to write this as: ((\hat{r} \times \vec{\nabla}) \times \hat{r})_i =...

Hi, I've been a lurker here for a while but I finally have a question. I was wondering if there is a simple formula to calculate the Color Rendering Index(CRI) and Correlated Color Temperature(CCT) of a white light source.. To do this I would also need (I think) to make a some points on a...

Homework Statement hey just wondering if anyone could show the the working for the index notation in the attachment it would be greatfully appreciated. thanks. the answer is there I am just looking for the working. Homework Equations The Attempt at a Solution

Homework Statement I am having trouble understanding how I would go about finding all subgroups of index 2 in R*, the multiplicative group of nonzero real numbers. Any hints will be greatly appreciated. Homework Equations The Attempt at a Solution

A glass rod seems to disappear when it is placed in vegetable oil. Based on this observation, predict the index of refraction for vegetable oil.

I'm differentiating with respect to Grassman variables, and I'm getting something very inconsistent: Suppose \xi and \chi are two-component, left-handed, grassman-valued spinors. Now, I take derivatives with of the product, \xi^a \chi_a, respect to \xi two different ways, and denote their...

Does the following identity hold?: \epsilon_{ijk} a_j b_k = -\epsilon_{ijk} a_k b_j

Oh btw, this is not a homework question! just got it somewhere. Light travels in a medium of n=1.2 at c1. what is its speed in a medium of n=1.6? a)1.3c1 b)0.67c1 c)2c1 d)1.7c1 e)0.55c1 my solution: using n=c/v, 1.2 = c/c1. also, 1.6=c/c2. c2= c/1.6. but c=1.2c1 So, c2=(1.2/1.6)...

refractive index... snell's law... help! Hi, im having a LOT of trouble with what seems like a basic question. i have been stressing over this for nearly 3 hours now. can anyone help me out? here it is: Light propagating from water into air is incident on the water surface at the angle of...

I am currently undergoing advanced higher physics and my investigation is on measuring refractive index. I have conducted 3 experiments so far: the standard ray lamp experiment from higher and two different versions of the apparent depth method. However, these experiments have been simple and...

Homework Statement Prove vector identity \nabla x\nabla\phi = 0 using index notation. Homework Equations \nabla x A = E[SIZE="1"]jrt\partial[SIZE="1"]rA[SIZE="1"]t The Attempt at a Solution I'm treating this as \nablax A, where A = del \Phi = E[SIZE="1"]tpq\partial[SIZE="1"]p\Phiq...

Homework Statement The glass core of an optical fiber has an index of refraction 1.62. The index of refraction of the cladding is 1.47. What is the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber? Homework Equations theta = sin ^-1...

Homework Statement Indicate the (111) and ([11]0) ([11] has an over line, so is negative, don't know how to do on forums!) planes in a cubic lattice in a diagram, then calculate the angle between them. The Attempt at a Solution I think I have drawn this right (see attatchment), but I am...

I'm studying Lie groups using G. 't Hooft's tutorial: http://www.phys.uu.nl/~thooft/lectures/lieg.html In page 34, he introduces superscript and subscript indices starting from equation 6.27: \phi_{\alpha} \rightarrow \phi_{\alpha}' = X_{\beta}^{\alpha}\phi^{\beta} What is the...

Homework Statement 1. The index of refraction for water is 1.33 and that of glass is 1.50. a. What is the critical angle for a glass-water interface?b. In which medium is the light ray incident for total internal reflection?Homework Equations nisin\varthetai=nrsin\varthetarThe Attempt at a...

In the problem of harmonic oscillator, for single mode, that is, the energy H = \hbar\omega(n + 1/2) It is easy to find the average of energy by considering the density operator <H> = \frac{Tr(He^{\beta H})}{Tr(e^{\beta H})} But for multimode (assume no polarization), we have to...

Hi, can anyone explain how miller indices can be determined for high index planes? For example, why is it that (544) = (S)-[ 9(111) x (100) ] I tried to figure it out but i could no find a pattern Thx in advance

[SIZE="2"]Homework Statement A beam of light is emitted 8.0 cm below the surface of an unknown liquid. The light beam is angled in a way that it strikes the surface 7.0 cm from the point directly above the light source. The light beam is totally internally reflected. What is the index of...

How does the refraction index vary with wavelength? For example, if you take light that initially has just one wavelength and disperse it through a prism and calculate the different indices for each wavelength. I'm guessing they'll be different... Is it linear? exponential? etc.

Homework Statement Let H and K be subgroups of G of finite index such that [G:H] and [G:K] are relatively prime. Prove that G = HK. The attempt at a solution All I know is that [G:H intersect K] = [G:H] [G:K]. What would be nice is if [G:HK] = [G:H] [G:K] / [G:H intersect K], for then I...

Hey guys, Sorry i coudln't find an appropriate forum for this topic, but I need to make index cards for some vocab words. It is much easier/quicker/neater if i were to type them on paper then cut them out like index cards. I only have the new word, i think its microsoft word 2008, and i can't...

Dear readers, In my recent study of dyadic products I found out that physical quantities expressend as 2nd rank tensors can also be expressed as a dyadic product of two vectors. Similarly 2nd rank tensor fields can be expressed as pointwise dyadic products of two vector fields. One such...

I was thinking about and I think it might be possible, but before I do anything stupid, anything have an opinion about this?

How does abstract index notation work? What do the the indices represent? I know the Lorentz transformation tensor in arbitrary direction, so if you want to use a specific tensor in an example, that would be a good one.

Homework Statement what is the minimum value that the index of refraction can have? Homework Equations n1sin\Thetai = n2sin\Thetar The Attempt at a Solution my choices are: A - between 0 and 1 B - +1 C - -1 D - 0 all listed values in my given chart are...

Finding index of refraction using wavelength and 2 angles?? I'm not sure how to do a problem that involves a light ray striking a block/air interface, how to find the index of refraction of a transparent material when given the wavelength, the angle the light ray makes with respect to the...

Suppose an experimenter firstly is entirely ignorant of general relativity and non-euclidean space. He finds (say) a point-source gravitational field. He fires light beams about and notices the deflection. He concludes that there's a not-equals-one index of refraction n about the source point...