Index Definition and 796 Threads

Show that if H is a normal subgroup of G of prime index p, then for all subgroups K of G, either (i) K is a subgroup of H, or (ii) G = HK and |K : K intersect H| = p.

Homework Statement Let G be a group and let H,K be subgroups of G. Assume that G is finite and that the indices |G:H| and |G:K| are relatively prime. Show that G=HK. Hint: Show that |G:H(intersect)K| is divisible by both |G:H| and |G:K| and then use the counting principle for |HK|.The Attempt...

Hi, does anyone know a link showing how to calculate curl with a Levi-Civita tensor. I can't figure it out but I am sure if I could see an actual example would be able to work out what is going on. Thanks.

In physics class we did an experiment where we dropped a metal pin in a beaker of water, covered half the beaker with a mirror and clamped another metal pin above the beaker. We had to find the refractive index of the water by measuring the apparent depth of the submerged pin and dividing it...

Can somebody tell me what is the miller index for the tilted plane? Is it (102) or (112)? Nothing seems to fit... I wonder if we can even describe it with miller index? Please download the picture here in pdf format: http://www.megaupload.com/?d=F8J344BH Thanks!

Homework Statement We learn from school that when we shine white light through a prism, dispersion occurs. This is because the light of varying wavelengths are refracted to a different extent due to how refractive index varies with the wavelength of light. So why does refractive index vary...

1. In an experiment to find the index of refraction, n, of a block of glass, the angle of incidence, θi, and angle of refraction, θr, were measured a number of times as follows: θi: 10° 20° 30° 40° 50° θr: 7.0° 13.5° 20.0° 25.5° 31.0° Given that the relationship between n, θi and θr is...

I was wondering how close 2 refractive Indexes have to be in order to be not visible? I currently have a glass fiber at 1.521 and am researching resin systems to match and so far have 2 - one at 1.506 and the other at 1.4736. I know which one is better (1.506), but is it close enough to...

I was wondering if someone can clarify the relationship between index of refraction and frequency. I know that when light is entering into a high index of refraction (say air to glass) that the index is increasing, light bends towards the normal, the speed decreases, and wavelength becomes...

Homework Statement Homework Equations Snell's Law: na*sin(theta of a) = nb*sin(theta of b) wavelength = index of refraction / n n = c / v The Attempt at a Solution The only information given in the problem is the 2 angles of refraction and of course n of air is 1, I do not understand how to...

Hi everybody! I have a question concerning tensors and hope you could help me :) http://www.rzuser.uni-heidelberg.de/~mbernha3/tensoren.pdf I would like you to look at expressions 13 and 16 :) I hope you won't be bothered by the fact the file is in German. I'm was wandering how these...

in relating the index of refraction to the relative permittivity (dielectric constant/function). it is known that n = \sqrt{\epsilon_r} for optical frequencies (i.e. \mu_r=1. now this website http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/diel.html#c1 gives the relative permittivity of...

http://www.measureofamerica.org/ & WOW is there some appalling stuff about the so-called "world's only superpower," if anyone cares. Here are some tidbits that stood out for the British media...

Homework Statement The light incident on a 45 degree prism undergoes total internal relfection at point P. What can you conclude about the index of refraction in the prism? (Determine either a minimum or maximum) This is a right triangle, with the two other angles being 45 degrees and...

I saw this pretty interesting article today: more... http://www.medicalnewstoday.com/articles/114271.php Here is more info on how to obtain the ABI: more... http://www.guideline.gov/summary/summary.aspx?ss=15&doc_id=5393&nbr=3696#s22 I'm pretty good at taking my own brachial...

for an example, polycrystalline silver, its index is n=0.135 and k =3.999 at the wavelength of 633nm, what does the nk mean, is that telling us the wavelength in the silver equals 633/0.135 nm ? and how to calculate the refractive angle in the metal? Give a good explanation, please.

Hi folks, Does anyone have a good reference for the refractive index of the near surface Martian atmosphere? (Or alternatively, the means to estimate it from readily available data!) I'm struggling to think of an equation for which I've got enough of the variables to be of use, (for...

Homework Statement The diagrams below illustrate the formation of a rainbow. Figure 1 shows the general arrangement and Figure 2 shows the path of a ray through a raindrop with the centre of the raindrop is labelled O. Figure 1: Figure 2: a.) Where the ray enters the raindrop in...

Can someone explain in terms of electric fields how the index of refraction squared = the dielectric constant of the material ?

And applying it to leading edge? research http://physicsbuzz.physicscentral.com/2006/10/string-theory-loop-quantum-gravity-and.html May be this is some what tongue in cheek? or are these theories open to crackpottery.

Homework Statement A slab of glass has a refractive index of 1.3. What will be the speed of light in this glass? Homework Equations The Attempt at a Solution \frac{sin i}{sin r}=1.3 ?

For Snell's law n2sin(theta2)=n1sin(theta1), I know that air has an index of refraction of approximately 1. But how do I find the actual value for the index of refraction if I know the temperature jump and pressure? I know that from what I am given, I can find the densities of the air, but then...

Hi, Can anybody please explain to me (in everyday language) what spectral index is? The wikipedia entry doesn't shed much light, and a lot of the textbooks give very convoluted explanations for its derivation. Thanks.

What does a higher index of refraction really mean? I know about speed wavelength etc but let's say you have 2 different material to choose and ignoring other variables, and focal length, diameter are all the same between both material, would you choose a lower index refraction or higher. Thanks

Homework Statement PART A) What is the frequency of blue light that has a wavelength of 450 nm? PART B) What is the frequency of red light that has a wavelength of 650 nm? PART C) What is the index of refraction of a material in which the red-light wavelength is 450 nm? Homework...

Does anyone have an idea about a formula relating the refractive index of a medium to the temperature gradient (Generally)?

?? Refractive Index ?? Dear all, For particle size distribution of MoS2 I need refractive index and absorption for this compound. Actually I couldn’t find it in the literature. Could you help me for this aim?

I've created a DLL that contains JavaScript plugins for the IE right click menu like this; http://img407.imageshack.us/my.php?image=20165640mt5.jpg I haven't restricted display to the proper context in the registry yet. In the Alt Text entry I have a small script that looks like; var altV...

Homework Statement A square(nxn) matrix is called nilpotent of index k if A\neq0, A^2\neq0,...A^(k-1)\neq0, But A^k=0 for some positive integer K Verify that A={{{021,002,000}}} is nilpotent. What is its index? Show that for this matrix (I-A)-1= I + A + A^2 The Attempt at a...

Could anyone tell me what the compression and expansion is used for in a Thermodynamics situation? What is the notation for Compression and Expansion in a formula? I am trying to calculate work done by a heat engine. Thanks

Could anyone tell me what the compression and expansion is used for in a Thermodynamics situation? What is the notation for Compression and Expansion in a formula? I am trying to calculate work done by a heat engine. Thanks

Which of the following statements are true? 1. The index of refraction is the ratio of the vacuum speed of light to the speed inside the medium. 2. The index of refraction is independent of the wavelength of the light. 3. If a light beam is incident perpendicular to the surface of another...

If I is empty, and the collection of sets {A_i} is indexed by I, then the intersection of all the A_i is equal to the universal set. Can someone explain why? Or better yet, give a proof?

hello everyone Consider extinction coefficient k, n becomes N=n-ik. the textbook says NsinA=N'sinB still holds itself. But the sinB,for exmple, may be a complex number, i want to know how to get B? how to understand this situation, which is the refractive angle? the B's real part?

Homework Statement An laser is used of wavelength 544 x 10^-7 m (in air) for eye surgery. The index of refraction of the fluid in an eye is n = 1.43. Calculate the frequency of the laser waves in the eye. n = 1.43 L1=544 x 10^-7 L2= f = Homework Equations n=L1/L2 L1 being the wavelength...

Homework Statement Find the dual vector of the following tensor: 6 3 1 4 0 5 1 3 2 Homework Equations dj= EijkTik Where Eijk = 1 if ijk=123, 231, 312 Eijk = 0 if i=j i=k or j=k Eijk = -1 if ijk = 132, 213, 321 The Attempt at a Solution Ok...

how these two are related to each there? if refractive index is given as a function of angular frequency, how both are related? reflective index= omega*c / k.anyone?

Refractive Index Units - URGENT - Homework Statement Does the Refractive Index of a medium have units. If so what are they? i am needing this for a lab report - so i can quote answers and feel fine that i am not giving any units. I am pretty sure there arent any.

http://aycu12.webshots.com/image/44931/2004851894362651280_rs.jpgany idea what then?

why some materials have bigger refractive index than others? Let's say why air have 1.003 refractive index, and quartz glass 1.46?

What does the "ff" mean in the index? I am browsing the index in Dummit & Foote and I notice that a lot of the page numbers have ff. after them. What does this mean? For instance, "Gaussian integers, 229ff., 271, 278, 289ff., 377"

Does anyone know where I can find a brief and useful description of the Witten index? The Wikipedia entry isn't bad, but didn't give me a real good understanding of it. (I have ascertained that for SU(N), the Witten index is N. Does this mean that SU(N) has N supersymmetric vacua, or that...

Homework Statement I'm taking a Magnetic Fields class, and the professor taught us doing cross and dot products using the permutation index. But I don't quite understand how it works completely. I have these problems: Given: \vec A=\hat x + 2\hat y - 3\hat z \vec B=3\hat x - 4\hat y...

1. If the index of refraction of you soap was 1.35, calculate the (minimum) thickness of the film at that part of the film that appears green, given that in air, green light has a wavelength of 535 nm. 2. x = L(lambda/2t) 3. I can't figure out how to derive the equation with n...

How can one measure refractive index by knowing the change in angular range of the first dark bands of an interference pattern(single slit diffraction), when the apparatus is change from air to under water? I think I missed that lecture, and I am still catching up.

Homework Statement For substance X, the refractive index is nx. For another substance Y the refractive index ny. Show that the refractive index for light passing from x to y is nx/ ny. 2. The attempt at a solution I'm finding it difficult to devise a solution, but I think the answer...

[SOLVED] Another Index of Refraction Problem! HELP! PLEASE Homework Statement When the rectangular metal tank in Figure 33-49 is filled to the top with an unknown liquid, observer O, with eyes level with the top of the tank, can just see the corner E. A ray that refracts toward O at the top...

Refractive Index Problem invloving prism (Please Help) Homework Statement What is given is a prism, angle of deviation and apex angle, I also have to find refractive index of the prism. To solve the problem I must prove that: [SIZE="2"]Nprism = sin((A+d)/2)/ sin(A/2) The diagram...

Hi, I recently read about the exciting research and progress being made with lenses made from negative refractive index materials. In theory, these materials have no limit to their resolving power and so far experiments have shown they can image objects smaller than that possible using...

I'm just don't get this question. from my text: define\ t_{mn}\ =\ \sum^{m}_{i=1}\sum^{n}_{j=1}|a_{ij}|, [a_{ij}\ is\ a\ doubly\ indexed\ array\ of\ real\ numbers.] (a)\ prove\ that\ the\ set\ \{t_{mn}\ :\ m,n\ \in\ N\}\ is\ bounded\ above. (b)\ use\ (a)\ to\ conclude\ that\ (t_{nn})\...