Index Definition and 795 Threads

both "mew"(sorry i couldn't get the symbol on on my keyboard so I'm writing it😊) and n are used for depicting refractive index i want to know which is more relevant and is there any reason for it or which symbol should be used in what cases.

Refractive index of a medium is defined as : n = c / v; v is speed of light in medium. I believe n is never measured directly as here is no way to directly verify c / v. So what I guess is that all refractive index values are experimentally measured using n = sin α₁ / sin α₂. But then there is...

The article https://www.bloomberg.com/news/features/2020-01-09/the-hidden-dangers-of-the-great-index-fund-takeover points out that 3 large index funds hold significant voting power in many US corporations and discusses possible effects ("dangers") that can arise from this. Another question...

I want to make an experiment about the refractive index of ice but this time I want to use different temperatures. (for example with -15 C ice and with -1 C ice) When I tried to search on the internet I couldn't find any specific formula or any article because I guess I couldn't explain what I...

I've been playing around with this for quite some time now this morning but can't get the last bit out. I defined the time functional to be $$T[y] = \int_{x_1}^{x_2} \frac{\sqrt{1+(y')^{2}}}{c(y)} dx$$ which follows from consideration of the time taken to cover an infinitesimal section of arc. I...

I emphasize that I am not posing a rhetorical question, and am not trying to make a political statement (and would ask all respondents to steer clear of politics), but would genuinely appreciate knowing whether the report in question is considered valid by those in the field who are impartial...

In the image attached, How is it that the angle shown is 2A? And what exactly is the position of min deviation? Why does it have to be in the given position as shown? Thanks in advance!

Since ##\nu## is contracted, we form the scalar product of the metric and inverse metric, ##g_{\mu\nu}g^{\nu\lambda} = (\vec{e_\mu} \cdot \vec{e_\nu}) \cdot (\vec{e^\nu} \cdot \vec{e^\lambda}) = \vec{e_\mu} \cdot (\vec{e_\nu} \cdot \vec{e^\nu}) \cdot \vec{e^\lambda} = \delta^\lambda_\mu## I...

Any one can help deduct the process to obtain the following equation? n= squart(ε*μ), n=refractive index, ε=relative permitivity, μ=relative magnetic permitivity. I am reading a book relating to spectroscopy, and saw the above equation. I am really interested how the scientists got this...

I was just thinking about this earlier and couldn't come up with a good enough resolution. I'm guessing it's a matter of convention more than anything. If we have ##x^{2} = a##, taking the principle root of both sides gives ##\sqrt{x^{2}} = \sqrt{a} \implies |x| = \sqrt{a}##. Yet evidently if...

A thin lens has an upper radius of curvature 𝑅1 and a lower radius of curvature 𝑅2. When the lens is completely surrounded by air, it has a focal distance 𝑓. The lens is then placed in the interface between air and water inside a vessel (see figure). Calculate the refractive index for the glass...

For finding refractive index of a glass block, we use n=real-depth / apparent-depth For calculating apparent depth microscope is raised vertically until a clear focus is obtained of the underlying mark beneath the glass blob. Given that microscope is perpendicular to the mark, Wouldn't the...

Apologies it's been a little while since I've done this, but I believe the rule is, that if the object is not a tensor you can not rename the dummy index? For example, i have the action ##\int d^3 x \epsilon^{uvp} A_u \partial v A_p ## and I want to write this in terms of the ##i## and ##0##...

A is the angle of refraction (~60 degrees) and Dm is the angle of minimum deviation that was different for each of the spectral lines associated to one of the six wavelengths measured. The problem I'm having is when I use equations of propagation of error to find the uncertainty in these...

Hey everyone . I was recently studying about fiber optics and it had a little to do with graded index fiber. And its given that the refractive index of the core changes from the axis to the cladding . So , my question is , how is that fiber designed ? It must be quite complicated to carefully...

I have a program where I am supposed to find out the pressure, given the ideal gas equation with Van der Waal's correction, $$\left(p - \frac{a}{v^2}\right)\left(v - b\right) \ = \ Rt$$I have to take a constant value for ##t## (user input), and ##v## will range from 1 to 20 in steps of 0.01. ##a...

Hi, I spent some time during my PhD with the task of indexing TEM diffraction patterns, usually made with selected area diffraction. All available software I found online was either too complicated or too expensive (or both). So I decided to make my own: https://www.odpin.com It's 100%...

The presence of the cosmological constant produces a flat spacetime universe with Ω = 1. There is also the curvature index of space k, which can be +1, 0, -1. But it is possible to have any of these values of k with Λ > 0 or Λ < 0. How is the curvature of spacetime determined by Λ different from...

Hi, I was doing this question and I was slightly confused as to whether I ought to just substitute n = \gamma (the adiabatic constant) into the equation? The answers don't do this, but I was wondering why it was wrong for me to do so? This was only a small fraction of the question (which was...

Lets consider the angular momentum tensor (here ##m=1##) \begin{equation} L^{ij} = x^iv^j - x^jv^i \end{equation} and rortational velocity of particle (expressed via angular momentum tensor) \begin{equation} v^j = \omega^{jm}x_m. \end{equation} Then \begin{equation} L^{ij} =...

Hi. I want to look up the H index of a few authors I am interested in using google scholar or some other site that i don't need to pay for access. But can't see how to do it. Can anyone help?

I have not seen anything published siting a value, so being the curious type I was wondering if any has and what is the value? Also it would be nice to know at what Energy it is referenced to Thanks all, Bob

The problem is multiple choice. A) refraction b) diffraction c) reflection d) dispersion An explanation would also be greatly appreciated!

Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...

Dear Sir/Madam, Is the product of the refractive index of a medium and speed of light in the medium equal to the speed of light in vacuum? Thank You.

Hello all, I would like to know which of the above two methods used in determining concentration of a solution is more accurate? Thanks, KV

I am trying to reproduce a very simple result that involved evaluating the refined index for a vector supermultiplet but ran into a snag. I hope someone will be able to clear that up easily. Apparently for a half vector multiplet (meaning that we do not include the CPT conjugated states), the...

Suppose I have a velocity field V^a which looks like < \partial x / \partial t , \partial y / \partial t , \partial z / \partial t > and I use the metric tensor to change it into a covector field V_a = g_{ab}V^a. Does it then represent the same quantity or < \partial t / \partial...

1. A light ray in dense flint glass that has an index of refraction of 1.655 is incident to the glass surface. An UNKNOWN liquid condenses on the glass's surface. Total internal reflection on the glass-liquid interface occurs for a minimum angle of incidence on the glass-liquid interface at...

how to write a summation with decreasing index say for adding from index 1 to n for $x_k$ we write $\sum^{n}_{k=1}x_k$. how do we write the above for index to go from n to 1 down wards

Hi, I know that, at least formally, the index of a radical should be positive and integer. That is if I introduce \sqrt[x]{2} I need to assume x\in \mathbb N and x>0. However, my calculator has no problem in calculating the radical for any x\neq 0, say x=-\pi. The result it gives is based on...

For class I conducted a experiment where I made sugar solutions, poured them into a glass prism container and used a laser pointer to find the refractive index. However, while typing in my results I realized I found the angle of deviation instead of the minimum angle of deviation since I didn't...

In Chapter 7: Hamilton's Principle, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, page 258-259, we have the following equations: 1. Upon squaring Equation (7.117), why did the authors in the first term of Equation (7.118) are summing over two...

I've been doing an experiment where I've used prisms and a spectrometer to find the exact angles inside the prisms and the refractive index of the prisms by finding the minimum angle of deviation. I have attached a picture of the formula I've been using to find the refractive indices. Where...

For the life of me, I can't figure out why my program won't update the index variable. I've tried setting the index to 0, and then to -1, and to the size of the arrayList - 1. I'm trying to use the index to get the previous and next flashCard in the arrayList to show up. I have been working on...

Consider a thin transparent plate surrounded by air. The plate's refractive index is exactly the same as the air's, but it does have a small loss (say of the order of 1%). Let the plate be vertical and normal to our "page" or your computer screen. A laser beam passes through the plate at an...

Hi. I came across the following statement , which seems wrong to me. Λμρ = ( ΛT )ρμ I have it on good authority (a previous post on this forum) that (ΛT)μν = Λνμ so I am hoping that the first equation is wrong ? It looks like the inverse not the transpose ? The equation Λμρ η μνΛνσ = ηρσ is...

Homework Statement [/B] In order for the refracted ray R to have the same direction in space as the incident ray I, shown above, which of the following conditions by itself would be sufficient? (A) n1=n2 (B) n1=n3 (C) n2=n3 (D) Plane surface P, is parallel to plane surface P2- (E) None of the...

Hello PF, I'm reading a paper for a project. In the paper they derive an equation for the effective refractive index ##n=\sqrt{\epsilon^{e} \mu^{e}}## of two stacked layers ##(n_1^2 = \epsilon_1 \mu_1, a)## and ##(n_2^2 = \epsilon_2 \mu_2, b)## where ##a,b## are the lengths and in my case...

red marker part in my book is very confusing. It says you will not succeed to create index by that. Is it trying to say that if we have two tables and there is a FK relation in them , then I won't be able to create index in either table? Can you please help with an example exactly when I...

Homework Statement we are asked to compare the graphs of 0.5^x with 2^x using index laws Homework Equations I am not sure how the regular index laws apply The Attempt at a Solution All I can say at the moment is the the graph of 2^x is a reflection of 0.5^x in the Y axis. I don't know...

Hi all, just had a question about tensor/matrix notation with the inverse Lorentz transform. The topic was covered well here, but I’m still having trouble relating this with an equation in Schutz Intro to GR... So I can use the following to get an equation for the inverse...

Homework Statement A monochromatic plane wave with wavelength 500µm is propagating through a dissipative medium with refractive index 1-0.0002i. It approaching the edge of the medium, and will pass out into free space. If the angle of incidence is not 90°, how much will the wave deflect as it...

Greg Bernhardt submitted a new PF Insights post The 10 Commandments of Index Expressions and Tensor Calculus Continue reading the Original PF Insights Post.

Hello I am doing some exercises in continuum mechanics and it is a little bit confusing. I am given the following equations ## A_{ij}= \delta_{ij} +au_{i}v_{j} ## and ## (A_{ij})^{-1} = \delta_{ij} - \frac{au_{i}v_{j}}{1-au_{k}v_{k}}##. If I want to take the product to verify that they give...

I am developing a FORTRAN code (.f90) which "ll calculate some matrix in some time interval (dt1=0.001) and these matrices have to be integrated in some time steps (dt=0.1). Though I am experience in FORTRAN 77, new to FORTRAN 90. I am unable to make dimension of matrix real (I think that is the...

By observing that red is the outermost color of the rainbow it is possible to conclude the refractive index of water, n, is lower for red than for blue. However, why is n lower for red? This seems to be answered by the Drude dispersion model, with a resonance in the ultraviolet region, but I...

Is there a limit to how steep a refractive index gradient can be before ray optics are no longer able to predict the path of the light? How is it related to wavelength? Under what conditions the light will be able to travel perpendicular to the gradient In a straight line? (having diffrent index...

Hi. I am working through some notes which use the following metric diag(1,-1,-1,-1). They give the 4-potential as ( Aμ ) = ( V/c , A ) where V is the scalar potential and A is the vector potential. This should mean in components A0 = V/c and A1 = A1 and so on but with the metric given shouldn't...

How does the relative permitivity and relative permeability related to the refractive index of a dielectic medium like water?