Geometrical Definition and 136 Threads

I'm searching for a week from now and can't find out difference between optical and geometrical length in optical path. Can anyone explain or give me idea or how can I find it out?

Homework Statement A sphere of radius 12.0cm has refractive index of 1.33. A speck is 4.0cm from the centre of the sphere is viewed along the diameter that passes thru the speck. Find the position of image when the speck is viewed from the nearer side? the ans is -7.2cm Homework Equations...

Hey, I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading. Starting with I = E / (4 * pi * r2) where E = original energy from source, we know that energy falls off as 1/r2, thus amplitude falls off as 1/r. From wikipedia: "The energy or intensity...

Hi there! I have the following property: If x(t) is a solution of \left\{ \begin{array}{l} \dot{x} = f(x) \\ x(t_0) = x_0 \end{array} \right. then the function y(t) = x(t+t_0) is a solution of the equation with initial data y(0) = x_0 . How could it be interpreted geometrically? Thanks!

How can I geometrically interpret this coordinate transformation (from x,y space to \check{x},\check{y} space)? x = \check{x}cos(β) - \check{y}sin(β) y = \frac{1}{2}(\check{x}2 -\check{y}2)sin(2β) -\check{x}\check{y}cos (2β)

Memorization, a contemptuous, futile, and insignificant method of learning math is, I think, not the solution to my problem. Well for the arithmetical progression, I have the formula: Let: l= last term a= first term d= common difference l= a+[d(n-1)] And for the geometrical...

In the following diagram find the distance d if a=4.0 mm, Θ=30° n_asinΘ_a=n_bsinΘ_b: snells law a^2+b^2=c^2: pythagorean theorem I think I got the angle to the problem correct. I am not sure if this is correct. Is this correct Θ_b=sin^-1(1sin30/1.52)?

A narrow beam of sodium light (λ=5893 A) is incident from air on a smooth surface water at θ=35°. Find the refraction angle and wavelength in water. n=λ_0/λ:wavelength of light in a material n_asinΘ_a=n_bsinΘ_b: snells law n=c/v:index of refraction I tried using the wavelength of light...

In a Goemetry book i read the following two axioms. 1) There exist at least two different points on each straight line 2) There is exactly one line on two different points But the 2nd doesn't imply the 1st axiom??

What is the geometrical shape called, when combining 3 ellipses together, such that each two share one focal point and together form a kind of 60 degree triangular shape? It will look similar to Reuleaux triangle, but it is not formed out of a triangle, but 3 ellipses, as if you are gluing...

Difference between Optical and Geometrical length!? I'm having this question since 2 times now in the theoretical part of the exam & still I couldn't find anything about it in the book neither in google. Can anyone who's more experienced in Optical Physics give me the answer to this please !?

In magnetism, the antiferromagnetic interaction between ising spin on a regular triangle is the simplest example of geometrical frustration. Is it possible that this frustration relieved for Heisenberg spins??

Homework Statement Can anybody explain how this compound can have 3 geometrical isomers isomers. <----------CLICK TO SEEHomework Equations NOThe Attempt at a Solution The compound contains two double bonds hence will have 2 pairs of cis-trans isomers.That means it will have four geometrical...

Can anyone give me a geometrical interpretation of the weyl curvature tensor?

Homework Statement A man stands 1.85m in front of a mirror hanging on a wall. His eyes are 10 cm below the top of his head. At what height from the floor, must the mirror be placed? Homework Equations Snells Law: n1*sin(omega)1=n2*sin(omega)2 The Attempt at a Solution I converted...

Hi friends, i have i request for you. For my statics exam i need integrals and i found this page in russian, and can not find rest or even know how it's called because when i translate title i don't get any results. Can you please help me and tell me where can i find the rest...

Homework Statement Suppose ABC is a triangle, where ∠ABC = ∠ACB =80°. A line BD through B meets AC at D such that ∠DBC=60°.Similarly CE meets AB at E where ∠ECB = 50°. Whats the value of ∠EDB? Homework Equations The Attempt at a Solution I solved the problem using coordinate...

I don't understand what the derivatives really mean?I know that they are the slope of the tangents drawn to a function.But see for example we have a function f(x)=x2 The derivative of this gives us '2x'. But what does '2x' mean?If i draw a graph of f(x)=2x what does it give me?what should i...

Hello all, i have frustrating task in my lab... i have to generate a code in MATLAB that will get the focal length and the object distance from the lens, i.e image (1000X1000 pixels). transfer it through the lens and, for the output it should be the result of it...

Homework Statement 1. A cylindrical tank 2.4 m deep is full to the brim with water. Sunlight first hits part of the tahnk bottom when the rising maes at 22o angle with the horizon. Find the tank's diameter 2. An aquarium is made from a thin-walled tube of transparent plastic 50 cm in...

What does it mean geometrically to say that V lies in span S, in other words that V is in a linear combination of S?

what is physical and geometrical meaning of limits?

Is geometric algebra and geometric calculus worth learning for a theoretical physicist? What are the advantages of this approach against the usual vector calculus ?

Hi guys. I am old person but not very old. I have a qustion that is very important for me to be answered. How can you cut simple geometrical shapes from a irregular solid using simple methods only? By simple geometrical shapes I mean cuboid, cylinder, pyramid and sphere. stuff like that. You are...

Q1 Two circles intersect at P and Q. Two parallel line segments APC and BQD are drawn to meet one circle at A and C, and the other circle at B and D. PB and PD are diameters of their respective circles. Prove that points B, Q and D are collinear. Q2 AB and CD are two parallel chords of a...

Hi PF! When Einstein was done with his General theory of Relativity, he was trying to build upon this theory, through different approaches, like the Kaluza-Klein theory, to try to build a classical theory of everything, which was purely geometrical. Since this wasn't successful throughout the...

Exists in mathematics a geometric figure, with straight lines (rectangle, parallelogram, or so), allowing you to determine the circumference and area of a circle by drawing / calculating / approximating? Without pi or formulas. So figure with no curved lines (and no polygons). for instance...

So I'm able to calculate them no problem. But the problem is, I don't really understand what they mean. For example, W=∫Fdr I understand that a vector field is something that defines a vector at every point. Then if we pick a curve in the field, we are integrating along that curve. So does...

Could anyone tell me what actually the geometric centre of a body is? please don't cite references from centre of mass or gravity.i want to know what it is in terms of its geometricity.

Homework Statement Dear Mentors, Please guide me in solving the circled questions on the 2 attachments. Homework Equations Thank you The Attempt at a Solution

Dear Mentors, Please guide me in solving the circled questions. Thank you

I would like to have a setup/software to geometrically simulate or represent the given molecule. For example I will input ; 2 hydrogen + 1 oxygen and it will output h2o and draw it's molecular shape. Also it would be much better if the software could give all the possible combinations of the...

Look at the picture below, I have to prove that the optical path length difference is \Delta=n(BC+CD)-BE=2nd\cos(r) [PLAIN]http://img200.imageshack.us/img200/2271/schermata082455775alle1.th.png The problem is just how to get 2nd\cos(r) I actually don't have any idea :\ I have...

In geometrical optics we consider that an image is formed at the point where two rays meet. But meeting of two rays will just create a change in intensity, that too will change according to phase difference. Also if the intensity say doubles it will make the image better visible but we...

Homework Statement We have triangle with sides d1,d2,l and angle \alpha between d1 and d2. Assume small change \Delta\alpha of \alpha. Homework Equations Then we can write for \Deltal equation \Deltal=(d1*d2)/(l) * sin\alpha\Delta\alpha. How can I prove that? The Attempt at a...

Homework Statement http://img857.imageshack.us/img857/3200/thedrawing00.jpg In a rectangle ABCD a square is built, EFGD, and a right triangle BMF, as described in the drawing. Given: DC = 60 cm BC = 40 cm The sum of the area of the square and the triangle is 784 cm2 Calculate...

The volume of the cylinder is 400 cm cubed. Calculate the surface area of a similar cylinder formed by enlarging the one shown by a scale factor of 2. The height of the cylinder is 10 cm. I don't know how to calculate the surface area, but I know that the area factor is (H/h)squared...

Homework Statement I have two problems- 1) A plano-covex lens is silvered on its plane-side and then it acts like a concave mirror of focal length 20cm. When the convex side is silvered it acts like a concave mirror of 7 cm focal length. What is the refractive index of the lens? 2) A...

N. David Mermin has an interesting geometrical approach to SR that I came across today. He seems to have described it in the following places: 1. Mermin, N. David, "Space-time intervals as light rectangles," Amer. J. Phys. 66 (1998), no. 12, 1077 2. a popular-level book called "It's About Time"...

Homework Statement What should be the focal distance of a negative thin lens such that there's a virtual image situated at 50 cm from the lens, of an ant at 100 cm from the lens? Given that the ant is at the right side of the lens, localize and describe the image. Homework Equations...

For some time I've been trying to get a geometric appreciation of why normed division algebras only exist in dimensions 1,2,4,8 (namely R,C,H,O). As always Baez provides the most elegant answer: http://math.ucr.edu/home/baez/octonions/node6.html" Allow me to descibe the key point of the...

"Open" and "closed" in the geometrical sense vs the thermodynamic sense Perhaps this is a silly question, but what is the relationship between the words "open" and "closed" in the geometrical sense (open, flat, closed universes) and in the thermodynamic sense (open and closed systems) in the...

We know the winding number as a curve winds round a point.If a point is inside a closed curve,then the winding number is 1,this is the geometrical intuition. The definition of winding number of closed curve gamma with respect to a is n(\gamma ,a) = \frac{1}{{2\pi i}}\int\limits_\gamma...

Could somebody explain to me please how to figure out a geometric description of a subspace? I understand how to check wether the set of vectors is a subset, but how t ogive them a geometric description?? lets say i have a subset in R3 {x: x3 = 2x1-x2} why the G.D. is a plane with an...

In discussions of questions related to gtr, it is often useful to know that one can in fact "create solutions to order" in gtr, when one wishes to model specific physical scenarios. Sort of, not really--- and herein lies a tale which illustrates some of the many thorny technical and conceptual...

Hello all, I am curious to know if any of you have ever used the Monte Carlo method to solve problems involving thermal radiation exchange. An overview of the problems that can be solved using this method is described here...

So I’m trying to visualize what is going on in QM geometrically. More specifically I would like to visualize the time dependent wave equation in 3 dimensions. So let’s start with dimensionality. Normally when I think of a function of some variables, I picture it in a space with the number of...

The notion of spectrum in algebraic geometry seem to be a bit abstract to me. Is it a set of points? Is it the analogue of spectrum in Fourier transform?

Hi! I am trying to find out where: cos\theta=\frac{a \cdot b}{|a||b|} came from. Here is mine geometrical interpretation of scalar projection: Now, (pr means projection) pr_{\overrightarrow{A}} \overrightarrow{B} = p\overrightarrow{B_0} and...

Geometry is arguably my weakest link in mathematics. The answers just don't "hit me" in geometry like some other sections of math do. When trying to prove something in a polygon, such as congruence of triangles made by segments etc. I find it difficult since the equal sides/angles aren't...