Index Definition and 795 Threads

Homework Statement Can I, for all purposes, say that Nabla, on index notation, is $$\partial_i e_i$$ and treat it like a vector when calculating curl, divergence or gradient? For example, saying that $$\nabla \times \vec{V} = \partial_i \hat{e}_i \times V_j \hat{e}_j = \partial_i V_j (\hat{e}_i...

I am following some lecture notes looking at the invariance of Poincare transformation acting on flat space-time with the minkowski metric: ##x'^{u} = \Lambda ^{u}## ##_{a} x^{a} + a^{u} ## [1], where ##a^{u}## is a constant vector and ##\Lambda^{uv}## is such that it leaves the minkowski...

Hi, I've somehow gone the past year without paying attention to the order of the indicies when one is upper and one is lower i.e. that in general ##g^{\mu}## ##_{\nu}## ##\neq g_{\nu}## ## ^{\mu}##. A have a couple of questions : 1) ##g^{u}## ##_{v} x^{v}=x^{u}## [1] ##g _{v} ## ##^{u} x^{v}...

I have always been a bit confused about how changing indices in a summations changes the resulting closed formula. Take this geometric series as an example: ##\displaystyle \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^n}##. Putting it into summation notation, we have...

Homework Statement I need to describe an experiment in which I would use internal reflection to determine the index of refraction of material Homework Equations Snell's law The Attempt at a Solution I understand the concept of internal reflection, such as the critical angle etc. I am just...

In an earlier thread, Science Vulnerability to Bugs, I mentioned the case Here is a similar case. In another recent case (can't find the link), an author decided to un-license his public domain contribution and withdrew it from publicly shared libraries, which broke very many products...

Homework Statement refractive index = 1.33 (water) real depth = 10m Homework Equations refractive index = real depth divided by apparent depth The Attempt at a Solution I'm going to call apparent depth X 1.33 = 10/x So I multiply 10/x by 10 so that i have x and 1.33 x 10 is 13.3... that's...

Homework Statement I shall be grateful if someone can help me understand this notation: http://files.engineering.com/getfile.aspx?folder=340bee11-1ba4-49b2-9a31-1a747012d69b&file=1.gif I know that this notation will finally/should finally give me the below six equations...

Hi PF! Which way is appropriate for defining del in index notation: ##\nabla \equiv \partial_i()\vec{e_i}## or ##\nabla \equiv \vec{e_i}\partial_i()##. The two cannot be generally equivalent. Quick example. Let ##\vec{v}## and ##\vec{w}## be vectors. Then $$\nabla \vec{v} \cdot \vec{w} =...

How can the radiation of electrons in the TRT be described/explained with transition between media of different refractive indices?

When I write \bigcap_\Delta M_\alpha I get $$\bigcap_\Delta M_\alpha$$ ... ...How do I get the index set $$\Delta$$ alongside $$\bigcap$$ as in the following text from Paul Bland's book "Rings and Their Modules" ... ... ?Hope someone can help ... Peter

Many textbooks and online sources give the relative permittivity of water as about 80 and the refractive index as 1.33. If you use the definition of refractive index to find the speed of light in water, you will find v = c/n ~ 2.56e8 m/s. However, if you use the equation to find the speed of...

Homework Statement This is from a old exam[/B] Humid air has a different refractive index than dry air: in the microwave region n'(dry) > n'(humid) and n''(dry) < n''(humid), where n' and n'' denote the real and imaginary part of the refractive index, respectively. How are the effects asked for...

Homework Statement A laser is fired into a wet paper placed ontop of a glass plate of thickness ##d## and an angle of ##0## degrees. When the light hits the paper and goes through the plate it forms a circle of light of radius ##R##. What is the index of refraction of the glass plate? Homework...

The question A microscope is focused on a black dot. When a 1.20 cm -thick piece of plastic is placed over the dot, the microscope objective has to be raised 0.380 cm to bring the dot back into focus. What is the index of refraction of the plastic Relevant equations/ideas...

Original Question (Please ignore this): I knew this when I read about it the first time a while back but can't put the two and two together anymore. :) I understand ##\vec{a_i}\centerdot \vec{a^j}=\delta_i^j## and ##g_{ij}=\vec{a_i}\centerdot\vec{a_j}## How does one get from there to...

What does "ff" mean (please see image below)?

In a crystal, the index of refraction is always calculated in the Lorentz oscillator model by examining the electronic response to an incident field and assuming a stationary nucleus. Is there however, any contribution to the index from the ionic nuclei in the background? I assume since I've...

Homework Statement Use index and comma notation to show: \begin{equation*}\text{div }(\text{curl } \underline{\bf{v}}) = 0\end{equation*} Homework Equations \begin{align*} & \text{(1) div } \underline{\bf{v}} = v_{i,i} \\ & \text{(2) curl } \underline{\bf{v}} = \epsilon_{ijk} v_{j,i}...

In Carroll, the author states: \nabla^{\mu}R_{\rho\mu}=\frac{1}{2} \nabla_{\rho}R and he says "notice that, unlike the partial derivative, it makes sense to raise an index on the covariant derivative, due to metric compatibility." I'm not seeing this very clearly :s What's the reasoning...

Homework Statement Find Fμν, given Fμν= (0 Ex Ey Ez) (-Ex 0 Bz -By) (-Ey -Bz 0 -Bx) (-Ez By -Bx 0) Homework Equations gμν =...

The index of refraction for a gas depends on temperature, as well as pressure. What is an experiment that would determine the temperature dependence of the index of refraction of air?

Hello I found a bug in my code and can't figuring out the error. I tried debugging by showing the output of each variable step by step but I can't find my error. Here is what I have and what I want to do: I have a matrix A: 0000 0101 1010 1111 And I have a matrix B: 10000 21000 30100 41100...

Homework Statement .[/B] I am attempting to determine the group refractive index of a laser cavity at it's resonance frequency. Homework Equations .[/B] \begin{align*} \frac{2\omega n L}{c} &= 2m\pi \end{align*} \begin{align*} n_g &= n + \omega \frac{dn}{d\omega} \end{align*} 3. The attempt...

Homework Statement I am trying to find the refractive index nylon (fishing line) , however when I used a laser onto the fishing line (nylon) it looked like it diffracted. Homework Equations I am able to find the diffraction if that was what it was showing, however I don't know how to calculate...

The statement that the higher the bandgap energy Eg, the lower the refractive index of material is confusing me. If I start from two equations. Eq1: Eg=hc/lamda_g Eq2: lamda=lamda_0/n Higher Eg means lower lamda_g. It means in order to have the light in semiconductor material with wavelength...

We have a monochromatic plane wave with a frequency ω=10^15 (1/s). It is spread in a medium whose resonance frecuency is also ω=10^15 (1/s). The wave is attenuated in the spreading direction. In 1 cm, the electric field of the wave is 10 times smaller. Give an expression for the extinction index...

How does the claddibg with lower refractive index reduce the light loss from the core? Thank you.

At the start of the chapter the book told me to use this formula to find refractive index: N= Sin(i)/Sin(r) How ever later in the section they showed me to use this formula when three quantities are given : NxSin(i)=NxSin(r) I tried apply the same method to a question, it gave me a wrong...

I am having trouble converting [D]=[A][ B]T[C] to index notation. I initially thought it would be Dij=AijBkjCkl but I have doubts that this is correct. Would anyone be able to elaborate on this? Regards

Homework Statement A thin converging lens has radii of curvature of R1=9cm and R2=-11cm. Assume its focal points F1 and F2 are 5cm from the center of the lens. Determine its index of refraction. Homework Equations Len's Makers equation: 1/f = (n2 - n1 / n1) (1/R1 - 1/R2) The Attempt at a...

Hi there, I have recently been researching in depth solar cells/panels, the parameters of their efficiency and the photoelectric effect in general, specifically how different wavelengths of light affect it. My research has yielded a few facts; that the efficiency of standard silicon solar cells...

Homework Statement Hey guys, I'm just going through a Laurent series example and I'm having trouble understanding how they switched the index on a summation from n=0 to n=1 and then switched the argument from z^(-n-1) to z^n as well as changing the upper limit to -infinity. If anyone could shed...

Homework Statement "Determine the polytropic process index 'n' from the initial and final condition parameters of the air (gas) in the air compressor cylinder." Im struggling with this question on my thermodynamics coursework and was wondering if anyone could help me out a little bit...

Does a BEC still have a very large refractive index for X Ray's and gamma rays?

Homework Statement prove grad(a.grad(r^-1))= -curl(a cross grad (r^-1)) Homework Equations curl(a x b)= (b dot grad)a - (a dot grad)b +a(div b) - b(div a ) The Attempt at a Solution Im trying to use index notation and get di (aj (grad(r^-1))j) =grad(r^-1) di(aj) +aj(di grad(r^-1))j which is...

I have studied about the formula of refractive index which is: . That means in the case of water which have μ =1 (approximate) and ε = 81, then n should be 9. But why we often use the value n = 1.33 for water ? Who can explain for me? I don't think the above formula is wrong, of course!

Hi everybody, I have a statistical problem in interpreting the index The variables for different indicators are taken from different population distributions and they might be recorded in different units of measurement. The values of these indicators are not quite suitable for combined...

Homework Statement Within a certain material, an EM wave with = 1 mm is attenuated to 10% of its original intensity after propagating 10 cm. Determine the imaginary part of the index of refraction ni Homework Equations 3. The Attempt at a Solution [/B] so...

Homework Statement Old photographic plates were made of glass with a lightsensitive emulsion on the front surface. This emulsion was somewhat transparent. When a bright point source is focused on the front of the plate, the developed photograph will show a halo around the image of the spot. If...

according to wikiedia i can express the index as n= √(εrμr) but i also know that the index of refraction depends of the wavelenght but i don't see any λ in the equation, so ... why?

Homework Statement Let's say we have a carrier signal xc(t) = AcCos(ωct) And there is a modulating signal or we can call it the information signal xm(t) = Am Cos(ωmt) and the modulation index is given as 0.8 How to write the modulated signal? It's really confusing as many people give different...

And what is the difference between refractive index and absolute refractive index? Why do we use relate two absolute refractive index to find the refractive index of a particular material say we need to find refractive index of water with respect to ice.and why do we always put the higher value...

Not sure if that's the technical name, but I refer the the number Excel give you between 0 and 1 when you use the "correl" command on two sets of numbers.

Hi I am currently looking at Newtons Rings, i have changed my refractive index to water (distilled), i have found the rings and they seem to be as aspected except they are extremely faint barely readable infact would anyone know a cause or soulation to this?

Homework Statement We look at the center of one face of a solid cube of glass on a line of sight making 55° with the normal to the cube face. What is the minimum refractive index of glass for which you will see through the opposite face of the cube? (Hint: see through will be possible if the...

Making sure I have this right, $ |A| = \sum_{i}\sum_{j}\sum_{k} \epsilon_{ijk}a_{1i}a_{2j}a_{3k} $ (for a 3 X 3) and a 4 X 4 would be $ |A| = \sum_{i}\sum_{j}\sum_{k} \sum_{l} \epsilon_{ijkl} a_{1i} a_{2j} a_{3k} a_{4l} $ ? Is there any special algebra for these terms? (they could be...

hi, I have studied the general expression for metamaterial as n=√(εμ) for dielectric relative permeability is one and we have n=√ε, but what would be the refractive index for magnetic material , by seeing symmetry I figure out as n=√μ will it be valid and we have Lorentz model for dielectric...

Homework Statement The antisymmetric tensor is constructed from a vector ##\vec a## according to ##A_{ij} = k\varepsilon_{ijk}a_k##. For which values of ##k## is ##A_{ij}A_{ij} = |\vec a|^2##? Homework Equations Identity ##\varepsilon_{ijk}\varepsilon_{klm} =...

Homework Statement Nobel prize for physics for blue laser diode using Gallium Nitride with band gap of 3.4 eV and a refractive index of 2.429. Explain how these parameters determine at what wavelength a Gallium Nitride semiconductor will laser at. Homework Equations E=\frac{hc}{\lambda}...