Index Definition and 795 Threads

Homework Statement I'm not sure if this can be answered without the picture but I can't get it posted. The problem gives theta(incident) and theta(r). It's a basic refraction through a transparent plastic piece. It askes for the index of regraction of this material. Homework Equations...

I am trying to build an index finger model but come to a problem, which I can not get over, on abduction/adduction movement at metacarpophalangeal(MCP) joint. Model description: My model is used to predict fingertip isometric force generation. There are 3 joints considered. There is two DoF...

This is for my 1st year undergrad course but it feels quite basic and not worthy of the 'Advanced Physics' section. Yet there's one thing I'm confused about - I have the answer, just something I don't understand. Homework Statement Light falls normally on a glass surface. What fraction of the...

Homework Statement At what distance below the surface of a lake will a fish have a 180 degree field view above the water surface (if the fish is looking up toward the surface of the lake) ? -Assume the index of refraction for water to be 1.33 and that of air to be 1.00 Homework...

Homework Statement Using your knowledge of perpendicularity between the reflected and refracted rays at the polarising angle, find brewster's law, a relation between Io (the angle to the normal) and the refractive index n. The relation consists of no other variable or physical constant No...

Variations in Refractive Index of atmosphere with altitude ?? The queries i have are related to refraction of light. 1. How does the refractive index of air vary with the altitude ? If possible explain the reason for change. 2. Does the amplitude of a wave change during refraction?

Homework Statement Index of refraction of air is being treated as 1, index of refraction for water is 1.33. W is given as 6.1 cm, the problem is to find H. Homework Equations By Snell's Law, n1sin\Theta1=n2sin\Theta2. We can also use at least one of the trigonometric equations...

I'm working on a piece of code to help me generate plots. Right now I'm focusing on the calculation stuff. Here's what I need to do. For each RPMline, calculate the Mach number (M0) for mdotf=.1,.2,.3,.4,.5,.6,.7 I read values of Tt4_Tt2_ratio, pi_c, eff_c, mdotcorr2 from the Excel sheet...

Homework Statement Let Y := \prod_{i \in I} X_i Now assume U_i \subset X_i to be open. If we take i to be infinite, \prod_{i \in I} X_i cannot be open. Why? Homework Equations The Attempt at a Solution I can't quite get my head around how to approach this problem. A...

My answer is: it is the relationship between the angle of incidence and the angle of refraction. Is it correct? If not, what should be the correct answer?

Just an urgent doubt, I am new to matlab. So imagine an equation that has two indexes, and that can be expressed as a matrix, how can I do something like this in Matlab? using a for cycle?

Homework Statement [PLAIN]http://img585.imageshack.us/img585/526/indexnotation.jpg The Attempt at a Solution How do I proceed?

Homework Statement I need to write w^2 in suffix notation for a derivation I am doing, where w = del X u Homework Equations (del X u) = w The Attempt at a Solution I think it is E[SIZE="1"]ijk([FONT="Comic Sans MS"]d^2u[SIZE="1"]k/[FONT="Comic Sans MS"]dx[SIZE="1"]j) where d...

Homework Statement I am supposed to verify that \nabla\cdot(\mathbf{u}\times\mathbf{v}) = \mathbf{v}\cdot\nabla\times\mathbf{u} - \mathbf{u}\cdot\nabla\times\mathbf{v}\qquad(1)[/itex] I want to use index notation (and I think I am supposed to, though it does not say to explicitly) to...

I'm just wondering how it works exactly? How can a solid submersed in a liquid somewhat "disappear". I've tried googling it with no luck and I'm super intrigued by this whole concept. PS: the more clear and simple you can explain it, the better.. I tend to get confused easily by things like this.

Homework Statement Find the index of refraction n of the rectangle using x, d, and θ. http://img338.imageshack.us/img338/6079/snellslaw.jpg Homework Equations n1*sin(θ1)=n2*sin(θ2) The Attempt at a Solution Is it possible to solve this problem given the relevant data? What I...

Homework Statement I was following along with a proof of AxB=-Bxa it went along the lines of; Let; C=AxB=Ciei D=BxA=Diei for i=1,2,3 and we know Ci=eijkAjBk Di=eijkBjAk we can manipulate B and A to give Bj=BsDeltasj Bk=AmDeltamk so we find; Di=eijkDeltasjDeltamkBsAm =...

Homework Statement If G is a finite simple group and H is a subgroup of prime index p Then 1. p is the largest prime divisor of \left|G\right| (the order of G) 2. p2 doesn't divide \left|G\right| I think I have this proved, but want to confirm my reasoning is sound. this problem is...

Homework Statement A light beam of wavelength 500nm travels from A to B in vacuum. (AB = 10mm) If we put a glass sheet with n=1.5 and 1mm thick, calculate how change the number of periods. Calculate the phase lag too. Homework Equations k0 = 2Pi/λ (vacuum) k= k0·n The Attempt...

First of all, sorry for bad english. Second of all sorry if such thread is already created, but I really need fast help.Homework Statement There's a lamp in the bottom of the lake. If you watch the lamp from the surface(out of the water) and your eyesight is crossed with the lake, you can see...

Hello everyone, I want to write in mathcad some critical temperatures and reduced temperatures using a range index (like in the document I've attached) and i can't figure how to do it (i'm new in mathcad) Is it possible to write those in this way? Thank you and sorry if i put the question...

Ca. 1996 a colleague bragged to me about an undergraduate lab he'd worked out where they did a high-precision measurement of g (I think he claimed 3 sig figs) using an index card, a pin, and a stopwatch. He didn't tell me any details. I've long since lost contact with him, but I was thinking...

Hi When we have a complex index of refraction, the real part determines the phase-change of the incoming wave and the complex part attenuates the wave. When we e.g. want to find the phase velocity using v = c/n, when should we use the real part of n or the modulus of n? Niles.

I get that the light changes speed as it enters a material with different densities, however I do not understand why a change in speed would cause a change in direction. For instance if I'm in a car and am going 55mph but slow down to 45mph I'm still going the same direction. It seems the only...

is it possible the refractive index remains constant while its extinction co-efficient rises as function of frequency? if yes when does this typical arise? i imagine that this can happen at the absorption edge of transmission spectra of a semiconductor but i don't find any explanation to this.

Snells law states that refractive index = (speed in medium 1)/(speed in medium 2) alternativley 1 μ2 = sin i / sin r Why therefore does Snells law also equal: μ1 * sin(angle-1) = μ2 * sin(angle-2) and for a critical angle μ1 sin C = μ2 sin 90 thanks

Can someone give me a precise definition of what an index set is? I have never seen it defined. Thanks!

Homework Statement This is complex analysis by the way. Here's the problem statement:http://i.imgur.com/wegWj.png" I'm doing part b, but some information from part a is carried over. The Attempt at a Solution My problem is that I don't know if I'm being asked to show it via direct...

Homework Statement This is from Henle's Combinatorial Introduction to Topology, section 9 question 2d). Here's the phase portrait: http://img69.imageshack.us/img69/70/phasepor.jpg Find the index of the point in the center of that picture.The Attempt at a Solution I used the fact that index =...

Dependence of refractive index on pressure Homework Statement Show that, in a gas (for which the refractive index is close to 1), the refractive index depends on the pressure as n_r = 1+ K\times p, and find the value of K. Homework Equations n_r = 1+ K\times p Clausius-Mossotti...

Dependence of refractive index on pressure Homework Statement Show that, in a gas (for which the refractive index is close to 1), the refractive index depends on the pressure as n_r = 1+ K\times p, and find the value of K. Homework Equations n_r = 1+ K\times p Clausius-Mossotti...

Is it true that if a finite group G contains a subgroup of index 2, then there is an element of G with order 2?

I am reading a paper where the author uses colons in the description of groups. Example (not verbatim): "This subgroup is isomorphic to (Z_5 X A_4):Z_2". Several subgroups are described in the same way (as (G_1 x G_2):G_3) throughout the paper. I have seen the colon in G:H to indicate the...

Hi everyone I'm having a bit of trouble solving this question. If anyone can help that would be awesome Homework Statement Rank the materials in the diagram according to their refractive indices from greatest to smallest (see attachment) The attempt at a solution The greater the...

Homework Statement In order to determine the refractive index of a transparent plate of glass, a microscope is first focussed on a tiny scratch on the upper surface and the barrel position is recorded. Upon further lowering the microscope barrel by 1.87mm , a focussed image of the...

Homework Statement If a star emits the same intensity of radiation at all visible wavelengths, what will be its apparent color at the Earth’s surface? Homework Equations No equations... The Attempt at a Solution I realize that a horizontal line would occur through the visible...

Homework Statement Prove the following: (\vec{r}\times\nabla)\cdot(\vec{r}\times\nabla)=r^2\nabla^2-r^2 \frac{\partial^2}{\partial r^2}-2r\frac{\partial}{\partial r} Homework Equations (\hat{e_i}\times\hat{e_j})=\epsilon_{ijk} (\hat{e_i}\cdot\hat{e_j})=\delta_{ij} The Attempt at a...

Homework Statement Using index notation to prove \vec{\nabla}\times\left(\vec{A}\times\vec{B}\right) = \left(\vec{B}\bullet\vec{\nabla}\right)\vec{A} - \left(\vec{A}\bullet\vec{\nabla}\right)\vec{B} + \vec{A}\left(\vec{\nabla}\bullet\vec{B}\right) -...

A ray of light travels through a medium with an index of refraction n_{1} and strikes an layered medium such that the index of refraction is n_{2}=ky+1 where y is the depth of the medium and k is a constant. If it hits at an angle of \theta_{1} with respect to the normal, find the angle...

hi All, Just wondering how you get the complex refractive index of a material from relectivity measurements at a single angle. I understand you must infer some of the data, using the Kramers Kronig relations, is this right? Is there a direct way of calculating it? I see from an article on...

http://spectrum.ieee.org/nanoclast/semiconductors/nanotechnology/nanostructured-metamaterial-enables-invisibility-cloak?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+IeeeSpectrum+%28IEEE+Spectrum%29 "We can even have amplification of light instead of its absorption. Here, for the...

Sry for a proper wall of text, and it´s probably pretty "chatty" too, as I reason about things back and forth... Plz do feel free to comment on the reasoning since I post it to learn how to think about these things... I believe that I have sometime learned that one can relate refractive index...

1- what determines the refractive index of a material? i understand that it is ratio between velocities in vacuum and medium but i want to know about complex refractive index which also accompanies extinction co-efficient. my explanation is that bent and slowing down of light depends on crystal...

Homework Statement 1.Given a set T we say that T serves as an index set for family F={Aa} of sets if for every a in T there exists a set Aa in family F. 2. By the union of the sets Aa, where a is in T, we mean the set {x l x\inAa for at least one a in T}. We shall denote it by...

Homework Statement Consider a cylindrical piece of material of a constant thickness d and radius r = a, but made out of a material with position-dependent index of refraction. How must the index of refraction vary with radial distance r such that the cylindrical piece act as a lens with a focal...

I'm probably doing something stupid here... A wave travels from a medium into a second medium with a smaller refractive index. By definition the speed of the wave increases. Then lambda*f = v, so the wavelength also increases. According to de Broglie, this means the momentum goes down...

Homework Statement A Lens maker desires to make a lens of focal length 30 cm. in air. The equipment in the shop is set to make lens faces of 20 cm. a. What index of refraction should the lens material have to produce this focal length? b. What would the focal length of this lens be...

!Logarithms and Index Laws help! Ive been trying to complete a revision sheet but it has logarithims and index laws, and i don't know how to do them. I've included a few of the hardest questions frome the revision sheet in the attachment. ...Look at attachment.... I've tried the...

Hi, I have an organic chemistry assignment identifying an unknown sample. My tutor has asked for the properties (I can find all but refractive index) for vanillin and p-bromobenzophenone. I found that for Vanillin it is 1.555 but I know that it changes with temperature and I cannot find a...

As a way to keep busy in between semesters I decided to work my way through Algebra by Dummit and Foote in order to prepare for the fall. Working my way through quotient groups is proving to be quite difficult and as a result I'm stuck on an exercise that looks simple, but I just don't know...