Index Definition and 795 Threads

Does a magnetic field refract when it enters into a different medium?

Assume we have a plane of oscillating charges described by x=xoei(omega)t. The total field is given by E=- \frac{\etaq}{2\epsilonc}i\omegaxoei\omega(t-z/c) . (Can someone point me to a website where I can learn to type in these formulas and not not have them suck?) Ignore that weird looking x^o...

Hi there, just wondering what this could mean: "Remark: AC is trivial for |I|=1, since A non-empty means \exists x st x \in A . Similarly for |I| finite (induction on |I|)." I is the index set. As in, our sets are {A_i with i in I}. I'm really not sure what this explanation is getting...

Racecar Winning Probability Index -- click to find out what it means So I just developed an equation that calculates how likely a racer is to win a particular race. It is not a probability ratio, which is why I'm calling it an index. RWPI(racer) = GRI(racer) / GRI(top competitors) where...

Does anyone know what gain guiding and index guiding mean in the context of lasers?

In MATLAB I have a function which calculates P04 for different values of i,j, and k providing a 8x89x89 matrix of values. I am trying to find the max P04 for each value of i and the corresponding j and k values. Here are my for loops: for i = 1:1:8; M1(i) = 2+0.1*i; for j = 1:1:89...

Maxwell theory n=\sqrt{\epsilon_r \mu_r Refractive index for water is n=1,33. For water \epsilon_r=81, \mu_r=1 so it should be n=9 Why we have so big anomaly for water?

Homework Statement Prove the vector identity: \left(a\times\nabla\right)\bullet\left(u \times v\right)=\left(a \bullet u \right)\left(\nabla \bullet v \right)+\left(v \bullet \nabla \right)\left(a \bullet u \right)-\left(a \bullet v \right)\left(\nabla \bullet u \right)-\left(u...

Homework Statement Define refractive index in terms of changes in the velocity of a wave in passing from one medium to another. Homework Equations The Attempt at a Solution Would I be right in saying that in terms of the question above, refractive index is the constant found between the...

The speed of light in a certain substance is 79.0% of its value in water. What is the index of refraction of this substance? Here's what I've done so far: (3.0*10^8 m/s)(0.79) because its 79%. In water, the n=1.003. I'm not sure where to go from there. Any help would be greatly...

Homework Statement A ray of light is incident in water on a plane water-glass boundary. The angle of incidence is 30 degrees. Calculate the angle of refraction. (Refractive index of glass with respect to air =3/2, refractive index of water with respect to air = 4/3). Homework Equations...

I'm thinking of normal dispersion, of course, far from any resonances, say in bk5 glass or water. I thought it might be due to higher-frequency light undergoing more collisions, but I'm not sure. Thanks!

Homework Statement While studying physics at the library late one night, you notice the image of the desk lamp reflected from the varnished tabletop. When you turn your Polaroid sunglasses sideways, the reflected image disappears. If this occurs when the angle between the incident and...

Homework Statement A light beam incident on a glass slide at an angle of 60 ˚, being partly reflected and partly refracted. It notes that reflected and refracted beams are each at 90 ˚ What is the refractive index of glass? Homework Equations n1sinσ1 = n2sinσ2 The Attempt at a...

Homework Statement After finishing your physics classes with the firm conviction that the questions were strange and out of touch with reality, you decide to take up spear fishing. While wading through water (of index of refraction=n and depth h) you spot a fish that appears to be a...

Homework Statement A laser beam enters a 10.0cm thick glass window at an angle of 30 degrees from the normal. The index of refraction of the glass is 1.46. At what angle from the normal does the beam travel through the glass? Homework Equations sin theta 1 / sin theta 2 = n1 / n2 = v1 /...

So I am trying to derive a formula from one of the standard summation formulas except starting at a different index. So if I have the series.. \sum i = \frac{n(n+1)}{2} Where "i" runs from 1 to n. (I don't know how to put it in the code.) If I want to make the series start from zero, I...

Homework Statement My question is very basic, yet one which has become increasingly frustrating. I am doing an investigation into determing the refractive index of Perspex for an assignment. To do this I am using a light ray box to shine a ray onto a rectangular perspex prism, and then using...

THe wavelength of a red helium-neon laser light in air is 632.8 nm. A) what is the frequency? ( i already figured this out to be 4.7 x 10^16) B) what is its wavelength in glass that has an index of refraction of 1.50?( i do not know where to or if i have to plug in the refraction into an...

Hi I'm trying to sort this concept out in my head and have reached a stumbling block! 1. ok so light travels through medium a and transmits through medium b and refracts. The angle or refraction is given by snell's law, and quantified by the refractive index of materials a and b. 2. But I...

Homework Statement what does the expression \delta_{ii} mean? Homework Equations \delta_{ij}=1 if i = j and 0 otherwise The Attempt at a Solution What I'm not sure about is if both indices are in the subscript does this mean i can only use it on a term with a subscript or can it also act on...

Where n >= 2. Is this true or false? I only got so far: If K is a subgroup of index 2, then it's normal. K is normal in Sn, so it's a union of conjugacy classes. Also, since |An K| = |An| |K| / |An intersection K| = 1/2n! * 1/2n! / |An intersection K| <= n!, then 1/4n! <= |An intersection...

Hello, Ok, I have been looking for a chart anywhere on the internet concerning the density of materials and the index of refraction. Wikipedia has one but it is just the different density of one type of glass vs index of refraction. I am looking for a chart with many materials and all their...

Homework Statement I uploaded the question below.2. The attempt at a solution At first what I did was using the Snell's Law formula n_1 \sin{\theta _1}=n_2 \sin{\theta _2} then I did this, n\sin{\ 45}=1 \sin{\ 90} so this is the minimum value that I got n=1.41 I'm not sure if my answer is...

If a beam of light enters water from air at 30 degrees from the normal. It then enters a glass block and exit into air. At what angle does it exit from glass to air ? My friend says it exist again at 30 degrees to normal. The refractive index of water is 1.3 and glass is 1.5.

Homework Statement Studying the mirage, we can assume that the index of refraction depends only on the vertical coordinate z. A ray of light starts from {0,0} with angle \beta\leq30. It's trajectory fits on an ellipse with major axis a and minor axis b. a) Give n(z)=? b) What is the trajectory...

What is the physical meaning of raising/lowering indexes? From a mathematical standpoint, I clearly understand what an expression like v_a = v^bg_{ab} means. But let's assume that v^a is, say, a 4-velocity: can I say that v_a is a 4-velocity as well? Or is it something different? Not to...

Okay, so I'm learning some basic index notation, and I have a few questions... Homework Statement f= scalar field F = vector field so, we are supposed to show that curl(fF) = fcurl(F) + (\nablaf) x F The Attempt at a Solution curl(fF) = [\nabla x (fF))]_{k} =...

Homework Statement Giancoli Ed. 6, Ch. 24, #52 One of the beams of an interferometer passes through a small glass container containing a cavity 1.3 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light...

When I was a little kid, I met a gemologist who showed me a cool trick with a ring he'd bought for his wife. When he submerged it in water, the crystal disappeared! As I now know, this crystal had an index of refraction of 1.33. Anyone know what this crystal is and/or how I can get my...

We have the index of refraction formula of n = \frac{c}{v} which essential states how much of a factor light travels faster in a vacuum than in this medium. Why don't they just have it as n=\frac{v}{c} so it states fractionally how much slower light travels in the medium than the speed of...

Homework Statement There are some equations in the notes on field theory I am reading with notation I have never come across before. Someone told me it was a way of ensuring that the expression was anti-symmetric. I can't find it used the same anywhere else but no explanation is provided...

Homework Statement A glass lens is coated on one side with a thin film of magnesium floride (MgF2) to reduce reflection from the lens surface. The index of refraction of MgF2 is 1.38; that of the glass is 1.50. Assume that the light is perpendicular to the lens surface and that the thickness...

as described in the title, what's the relationship between these 2 quantities in a given material? ty

list of index notation properties ?? Is there a list of index notation properties somewhere on the web ?? I'm just looking for a pdf file that I can reference while manipulating tensors using index notation (and summation convention). I'm not looking for proofs at all, just a quick...

A ray of light strikes a square glass block at an angle of 45 degrees and enters the glass. If this block is surrounded by air (n=1), what is the minimum value of the refractive index of the glass if the total internal reflection occurs at point P. (see attached diagram) I'm really lost on...

Homework Statement Is there any way to calculate a solution's concentration (mass percentage - that is, the percentage of the solute mass to the solution mass) just by knowing its index of refraction? If it helps, the solute is NaCl, so I know the molar mass of the solute. I also have the...

[SOLVED] Index of refraction Homework Statement An air bubble inside an 9.00 cm-diameter plastic ball is 2.90 cm from the surface. As you look at the ball with the bubble turned toward you, how far beneath the surface does the bubble appear to be? Homework Equations n_1/s + n_2/s' =...

Homework Statement To a fish in an aquarium, the 4.30 mm-thick walls appear to be only 3.10 mm thick. What is the index of refraction of the walls? Homework Equations m=-s'/s n_1/s + n_2 / s' = (n_2-n_1)/R m: magnification s: object distance s': image distance The Attempt at a...

w=∇×u Is this correct? w_i=ε_ijk ∂/(∂x_j ) u_k w and u are the vectors C=(x∙y)z Is this correct? C_i= ∑_i〖(x_i y_j)∙z_i 〗 C, x, y, z are vectors A^T∙A ∙x=A^T∙b Is this correct...

Homework Statement Prove the following relationship: \epsilonpqi\epsilonpqj = 2\deltaij Homework Equations The Attempt at a Solution All I have so far is the decomposition using the epsilon-delta \epsilonpqi\epsilonpqj = \epsilonqip\epsilonpqj \epsilonqip\epsilonpqj =...

Homework Statement A beam of light is split into two coherent beams of intensity I which are in phase. The two beams are sent through different paths and superimposed at the same spot on a screen. A path difference is to be achieved by inserting a glass window of refractive index of 1.7 in the...

I have a question regarding the attached file. How do you get those indicies when you multiply the kronecker deltas with A, B, and C? For instance, C - subscript m remains the same on the left side of the expression, but then becomes C subscript i on the right side. How does this logically...

I'm new to the forum, so, hi =D Special theory of relativity tell us that the speed of light is the same, independently of the reference frame. But we know that, while light travels through some materials (with refraction index larger than one), it speeds slows down. These two "things"...

Can you please help me sort out my terminology? Are 'power', 'index' and 'exponent' exact synonyms, even thogh they tend to be used in different contexts? If a^x gives 'exponential growth' is the growth described by x^a also properly called 'exponential'? If not, what is it called...

Light strikes the surface of a transparent material at an angle of incidence of 30. If the refracted angle in the transparent material is 20, what is the speed of light in the material? Is it possible to solve this problem without their index of refraction? If possible, how?

Hi everyone! I am trying to self- study GR and I am (very slowly) working through Schutz at the moment ( not the clearest at times for a " first course" text). Anyway I have noticed that several times when working with components of physical variables e.g. momentum/ energy, the 'up' index in say...

I have a general question about index notation. For an arbitrary quantity, a, "a" denotes a scalar quantity. "a_i" denotes a vector. "a_ij" denotes a 2nd-order tensor. So, if I have something like "a_i*e_ij*b_j" Would this be like multiplying an nx1 vector, an mxm matrix, and an Lx1 vector...

what is the obvios differences between p-type substrate of having Miller index of (100) and (111), beside (111) plane have higher atom density?

Homework Statement 5) A beam of monochromatic light enters an equilateral triangular prism at an angle of incidence of 30.0º. If the index of refraction of the prism is 1.53, at what angle with respect to the surface of the prism does the beam emerge from the other side of the prism...