Index Definition and 795 Threads

Hello all, long time lurker, first time poster. I don't know if I am posting this in the proper section, but I would like to ask the following: In index notation the term σ_{ik}x_{j}n_{k} is \bf{σx}\cdot\bf{n} or \bf{xσ}\cdot\bf{n}, where ##σ## is a second order tensor and ##x,n## are vectors...

Consider an interface along x-axis which separates two media. The medium below y = 0 is air or vacuum and light is incident from this medium onto the surface. The refractive index of the medium above y = 0 varies with x as some function of x : μ = f(x). Does the Snell's law still hold good ?? If...

Homework Statement A beam of light is reflected from the surface of some unknown liquid, and the light is examined with a linear sheet polarizer. It is found that when the central axis of the polariser (that is, the perpendicular to the plane of the sheet) is tilted down from the vertical at an...

Hi. I'm just starting QFT for the first time. I've just finished a course in relativity but I'm confused about the index notation I've found in QFT. Here are 2 examples yi = Σ Mij xj and yj = δij yi . These examples don't seem right after what I have learned in relativity unless the index...

First of all, I'm sorry if this is not the right place to put this, but I thought it would be relevant to a science/math resources forum (so feel free to move this or do whatever). One idea I was considering is if there could be a thread that contained an index of important things that one...

If you're using a phase contrast microscope and the refractive index of the medium is equal to the refractive index of the cell, what are you able to see? I guessed that you wouldn't see anything, but apparently that's wrong. The only options are membranes, vesicles, the nucleus, pigment...

Homework Statement The prisms have a refractive index ##n_1=1.3## at wavelength ##\lambda=300nm## and are connected by a material with refractive index ##n_2##. What is the refractive index ##n_2## so that light of wavelength ##>\lambda## follow path 2, and light at ##<\lambda## follow path 3...

Homework Statement A light ray enters the atmosphere of the Earth and descends vertically to the surface a distance h = 101.2-km below. The index of refraction where the light enters the atmosphere is n = 1.00 and it increases linearly with distance to a value of n= 1.000293 at the Earth's...

I am having trouble showing that ##(A_{ik}B_{kj})_{mm} = (A_{ki}B_{jk})_{mm}## Wouldn't the right side end up having a different outcome? Or can we assume its symmetric?

I am confused at why ##V_{i,j}V_{j,k}A_{km,i}## the result will end up being a vector (V is a vector and A is a tensor) What are some general rules when you are multiplying a scalar, vector and tensor?

Hi. Got 2 more questions on index placements. 1 - I found the following on an exam paper and it seems wrong to me. It concerns a weak perturbation to the Minkowski metric gik = ηik + hik. It then states that to first order in hik the contravariant metric tensor is gik = ηik - ηinηkmhnk. This...

Can anyone explain how to take the derivative of (Aδij),j? I know that since there is a repeating subscript I have to do the summation then take the derivative, but I am not sure how to go about that process because there are two subscripts (i and j) and that it is the Kronecker's Delta (not...

1. The problem is: ( a x b )⋅[( b x c ) x ( c x a )] = [a,b,c]^2 = [ a⋅( b x c )]^2 I am supposed to solve this using index notation... and I am having some problems. 2. Homework Equations : I guess I just don't understand the finer points of index notation. Every time I think I am getting...

Homework Statement I have set up an experiment such that microwave is converged and beamed to a polymer slab and the reflected wave is measured. I have recorded angle of incidences from 15 to 90 degree and I found out that at 80 degrees, the output is the highest, while at 45 and 85 degrees...

Hi 1)Does refractive index varies when we are dealing with different waves? for example the refractive index for a typical glass is 1.5 when a visible light passes through it. Does it the same for x rays? 2) there is a complex formula which describes the refractive index: n = 1- δ - iβ. how is...

When white light is refracted in a prism, we can see that blue color has the strongest refraction: the shorter the wavelength, the strongest the refraction. But the electromagnetic radiation with very short wavelength (X-rays) are not refracted by an amorphous solid such as glass: most part of...

Homework Statement Hello! Please, take a look at the picture attached. I would be grateful for the step by step explanation of the math equation; how it has been derived from f/s (1 + libor eur) - (1 + libor dol) to the one with logs? Homework EquationsThe Attempt at a Solution Thank you very...

Hello All, I am having some issues with calculating the measurement uncertainty when there is a mismatch in the index of refraction between a fluid and an interface. If am using an unobtrusive measurement technique such as Laser Doppler Velocimetry, how would I be able to quantify the...

Homework Statement So I'm currently modifying an example Symbolic Regression program that uses genetic programming, a type of evolutionary algorithm. I'm using the python deap library. Not sure if anyone on here is familiar with it, but I think that the error is more general to a misuse of...

Index notation in GR is really confusing ! I'm confused about many things but one thing is the order of index placement , ie. is Λa b the same as Λba ? And if not what is the difference ? Thanks If anyone knows of any books or lecture notes that explain index gymnastics step by step...

Homework Statement From an uniaxial crystal, a 0.7 mm thick plate is cut out in a way that the optical axis is parallel to the surface. A light falls perpendicular to the surface (circular polarization) with 500 nm. After the crossing of the plate, the light has elliptical polarization and the...

Hello I have an optic problem I want to calculate absorption index I know transmittance by 90% ;refraction index to material 1.586 ; thickness 2 mm ; power of source 21 lm

The General Relativity text I am using gives two forms of the Electromagnetic Energy Momentum Tensor: {\rm{ }}\mu _0 S_{ij} = F_{ik} F_{jk} - \frac{1}{4}\delta _{ij} F_{kl} F_{kl} \\ {\rm{ }}\mu _0 S_j^i = F^{ik} F_{jk} - \frac{1}{4}\delta _{ij} F^{kl} F_{kl} \\ I don't see how these...

Greetings, Do we use Absloute refractive index when finding crtical angle ? if it was two mediums ( not vacuum or air) how would i calculate the critical angle ? I mean i get confused when I find relative refractive index because sometimes i get sine inverse greater than 1 which give no...

Homework Statement Prove the following: ##(\partial_{\mu} \phi)^{2} = \dot{\phi}^{2} - (\nabla \phi)^{2}##. Homework Equations The Attempt at a Solution ##(\partial_{\mu} \phi)^{2}## ## = (\partial_{\mu} \phi)(\partial_{\mu} \phi)## ## = (\partial_{0} \phi)(\partial_{0} \phi) +...

Can you show me as explicitly as possible through equations?

Homework Statement I've uploaded a diagram showing a two beam interferometer that can be used to monitor changes of refractive index in a gas cell. it is illuminated with monochromatic light of wavelength λ. The light is linearly horizontally polarised. The two polarizing beam splitters (PBS)...

Homework Statement There are three subquestions in this question, all marked bold. Let's consider a gradient index lens of thickness ##d##, whose refractive index changes with the distance from the axis with the following formula $$ n(r) = n_1 + a r^2 $$. Determine the lens's focal length...

I have the expression ##g_{ab}=\eta_{ab}+\epsilon h_{ab}##, The indices on ##h^{ab}## are raised with ##\eta^{ab}## to give ##g^{ab}=\eta^{ab}-\epsilon h^{ab}## I am not seeing where the minus sign comes from. So I know ##\eta^{ab}\eta_{bc}=\delta^{a}_{c}## and...

Hi, I am a first time poster and I am completely lost with this question. Any help would be greatly appreciated Filling the space between a contact lens and the cornea is a small quantity of liquid of refractive index of 1.336. Assuming the refractive index of the lens material is 1.490 find...

I am reading some of "Planck 2013 results. XXII. Constraints on inflation." The paper is full of values for various inflationary parameters under various models, with their confidence intervals. For instance, in Table 5 on page 13, the authors report that — for a model including both running of...

I'm not sure if this step on my calculation is correct or not...

Homework Statement Homework Equations Snell's Law n1sin(theta_1)=n2sin(theta_2) Total Internal Refraction: sin(theta_c)=(n_2/n_1) lambda_n=lambda_n The Attempt at a Solution So I drew the triangle and this is what I got, and well here is just a picture so far of what I have. [/B] I've...

How can I control the refractive index on a material, I mean on what depends the refractive index? Because I am trying to create like a controlable light diffuser mechanism. Thanks and regards.

Is there any relation between refractive index and polarization?

The refrative index law should be sine(i)/sine(r) but in the answer he done the opposite. I included the answer in the bottom of the question.

Suppose we have a general timelike congruence of curves with tangent vector field ##V##, then the standard decomposition of the covariant derivative in index form (see e.g. Hawking and Ellis' "Large scale structure of space and time" equation 4.17) is given by $$V_{a;b} = \omega_{ab} +...

I am learning sky wave propagation and in my book, a relation between refractive index, dielectric constant and electro field strength is given. \mu=\mu_0\sqrt{1-\frac{Ne^2}{\epsilon_0m\omega^2}} Is this a form of Kerr opto-electric effect? How do you get this expression? If you think I cannot...

Hello all, whether the Refractive index of piezoelectric materials (Example: Polyvinylidene fluoride-PVDF ) changes by the application of pressure, strain or force ?

Homework Statement Suppose, light is passing through a liquid whose refractive index is time-varying. What will be the path of light ray ? Will it be a straaight line or curve ?Homework EquationsThe Attempt at a Solution I think, it will be a straight line.

I am making mess of the following expression.. i have following expression ## \frac{\partial{g}}{\partial{g_{\mu j}}} *g_{\nu j}=g \delta^{\mu} _{\nu} ## then I have sum over j only in the above expression. But above expression is nonzero only when ##{\mu}## is equal to ##\nu##. So we have ##...

Homework Statement Unpolarized light hits a flat glass surface, 37.5 degrees to the surface's normal. The reflected light's polarization is investigated with a polaroid. The relationship between the max and min value of intensity from the polaroid when it is rotated is 4.0. What is the index of...

I need to calculate the refractive index of a semiconductor material over a wavelength range (1×10-5m - 1×10-9m) and with different values of electron and hole carrier concentrations (i.e. n/p doped). I found this equation that relates those parameters: n+ik = √ [ (εm -...

Hello All, I would like to start learning how to ray trace but the tracing through a tube with a thickness of t has got me stumped. If I have an n1 (outside tube), n2 (Tube), and n3 (inside tube). n1≠n2≠n3. Knowing Θ1 (the angle of incidence in relation to the normal), I can calculate Θ2 from...

1.Problem: A vessel is quarter filled with a liquid of refractive index A. the remaining parts of the vessel is filled with an immiscible liquid of refractive index 3A/2. The apparent depth of the vessel is 50% of the actual depth. the value of A is? 1)1 2)3/2 3)2/3 4)4/3 Solution: 1...

Hi, I want to translate this equation R_{\hat{n}}(\alpha)\vec{x}=\hat{n}(\hat{n}\cdot\vec{x})+\cos\left(\alpha\right)(\hat{n}\times\vec{x})\times\hat{n}+\sin\left(\alpha\right)(\hat{n}\times\vec{x}) to index notation (forget about covariant and contravariant indices). My attempt...

I was reading my lecturer's notes on GR where I came across the geodesic equation for four-velocity. There is a line which read: Summing them up, \partial_i g_{aj} u^i u^j - \frac{1}{2} \partial_a g_{ij} u^i u^j = \frac{1}{2} u^i u^j \partial_a g_{ij} I'm trying to understand how LHS = RHS...

Homework Statement A ray of light passes through a prism, making the minimum angle of deviation. The rays enter and emerge at 37degree from the normal to the surface. What is the index of refraction of the material, if the prism angle is 50degree?[/B]Homework Equations...

Homework Statement (a) Find matrix element ##M_{ij}## (b) Show that ##x^j## is an eigenvector of ##M_{ij}## (c) Show any vector orthogonal to ##x^j## is also an eigenvector of ##M_{ij}## Homework EquationsThe Attempt at a Solution Part(a) [/B] \frac{\partial^2 \Phi}{\partial x^i x^j} =...

Hello all, I had clarified that refractive index of material such as(aluminium, copper, lead, teflon)changes with the temperature. the refractive index change even for this temperature range: -196 to 25°C ? I need to know like any law which gives a direct relationship between 1)the density and...