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4

A "sharp" tip typically has a finite curvature; there will be a very small part of the "tip" that is therefore angled at such a way that light will be reflected off it. The sharper the tip, the smaller the radius of curvature, and the smaller the "twinkle" or glint. The second effect is diffraction: Light that passes an object will be diffracted. For ...


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The easiest method is to use the transfer matrix: http://en.wikipedia.org/wiki/Transfer-matrix_method_(optics) Your question is actually related to a recent Science paper: http://dx.doi.org/10.1126/science.1249799


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Basically it means that in the case of OAM=0 the wave fronts make a structure similar to a stack of plates, and in the case of OAM=1 they make a helix-like structure, and 1 refers to the helix multiplicity (for a double helix it would be 2 and so on). One cannot be changed to the other continuously, so this is a topological feature. There are other ...


3

If I understand the question correctly, you are asking at what height light would be able to travel in a circle around Earth due to refraction. This would be the height at which the optical path length ($OPL$) of this circular trajectory as a function of height has a local minimum. This optical path length would be given by this formula: $$ OPL=2\pi r \cdot ...


2

The manufacturer generally specifies a cutoff wavelength for single mode optical fibre designed for specific wavelength. For example, a single mode fibre desgined for 700nm would have a cutoff wavelength few tens of nanometers below 700, lets say 680nm. What this means is that at cutoff wavelength, the Normalized Frequency or the V-number would be exactly ...


2

While our definition of the meter is based on the speed of light, our definition of length is not. Naming and defining a unit of measurement is entirely different than defining a physical quantity. The most natural way to define distance (known by physicists as proper distance) is the measured spatial separation $\Delta r$ between two points in space. Rigid ...


2

Refractive index describes the speed of propagation of light in a medium. So to restate your question: why is the speed of light slower in some media than in others? The wave equation tells us that speed of propagation depends on two factors: one is an inertial term, while the other is an elastic term. Let's look at a simple case of a string. The ...


2

The problem here isn't a simple algebra error, but rather an issue with the physics. A medium which at rest is isotropic no longer behaves as an isotropic medium when it is moving relativistically. Instead, it behaves as a nonreciprocal bianisotropic material. In particular, the phase velocity of light at a particular frequency in a medium is no longer ...


2

First of all, this is NOT a 2D photonic crystal since you send light in the $z$-direction (you are using all 3 dimensions) and if the rod is not infinitely long. I'm not aware of an analytic formula, but your band diagram exhibits several features characteristic of metallo-dielectric photonic crystals. For example, there's a bandgap starting at zero ...


2

The Magnification is a combination of all of the focal lengths of the picture you have shown above. A real image is created by the objective and tube lens. This creates an image of what you have at the object plane that is magnified by: $M = \frac {f_{tube lens}}{f_{objective}}$ So, if you were to measure the size of the image, it would be M times ...


2

A telescope with two convex (converging) lenses is a Keplerian telescope. The lens with the longer focal length is the objective, and the shorter focal length lens is the eyepiece. Since it is explicitly stated that the lenses are thin, you can use the thin lens equations: $$ \frac{1}{d_i} + \frac{1}{d_o} = \frac{1}{f} $$ where $d_i$ is the distance to the ...


2

You can think of super massive object like black holes which can bend light. Near the event Horizon you could get a 180 degree turn for light and thus see the earth back in time. But I do not think this is practically possible as earth is small and dark (compared to stars) and this layer would get compressed really thin as some small deviation in the ...


2

This may (or may not) lead to the same answer as CuriousOne's suggestion above, but the most appropriate (and the longest) way of attempting a solution would to be to employ the Fermat's principle. The method's nicely described in the link, but in a nutshell, you would be led to a condition of the type $$\delta \int n ds = 0$$ where this $ds$ can be cast in ...


2

There is no theoretical upper limit. The question is whether the description has any practical use. Real-world objects will have some small deviations from the perfect sphere or cylinder shape, for which Mie theory applies. Look at the polar diagram of scattering of red light from a 10 micron water droplet. Figure 2 in ...


2

I would say that it depends on your application. If the beam is small compared to the clear aperture of the lens, then you can probably treat it as a thin lens without any trouble. If the beam is large, you will probably have to treat the rays differently depending on their distance from the optical axis. IIRC you won't be able to use a transfer matrix for ...


2

Assuming the two surfaces are still spherical, you can still use transfer matrices to treat a thick lens. Citing the Wikipedia article on transfer matrices, the transfer matrix for a curved interface is $$ I_C(n_i,n_f,R) = \begin{pmatrix}1&0\\\frac{n_i-n_f}{n_f R}&\frac{n_i}{n_f}\end{pmatrix}. $$ The ray matrix for translation is, as usual, $$ ...


1

It depends on where you are standing. A convex surface is one that bulges out towards the person who is talking about it. Since we do not live inside glass, everyone knows what a bi-convex glass lens is - one that bulges out on both sides as seen by someone who lives in air. Note that while it bulges out towards the incident ray arriving from the air, the ...


1

I'm sorry, but your formulas do not seem correct. First, the NA is defined in free space, not inside the fiber. So, NA = 0.22 means that is the NA in air. Therefore, the angle is $sin(\theta) = 0.22 \rightarrow \theta = 12.7 deg$. [no need to divide by the index of refraction] Next, NA refers to the half angle, not the full angle (see: ...


1

We cannot multiply light by mere reflections, because the very definition of "reflection" means that the same light comes out. We can however multiply light by letting it pass through special materials which we "pumped" into a certain state, that's called Laser. And yes, a Laser design includes a sequence of reflections, but it is not the series of ...


1

Fundamentally, yes. One needs to break the time-reversal symmetry by either introducing a magnetic effect or modulating the "glass-like" materials dynamically. Practically, this is a very active research area. One could, for example, inject carriers into silicon dioxide at a very high frequency to achieve the one-way effect.


1

Misaligning one of the end mirrors will produce a set of vertical or horizontal fringes at the detector plane (depending on the misalignment of the mirror). The number of fringes is proportional to the misalignment angle of the mirror and inversely proportional to the wavelength of the light. When first setting up the alignment of the interferometer, this ...


1

Do you mean that the spot on the mirror where you see the image changes? That's not the location of the virtual image. The location of the virtual image is not on the mirror, it is behind the mirror, at the location the box would have if 1.) your mirror were clear transparent glass and 2.) the box were really behind the mirror instead of in front of it. ...


1

Try this experiment: take a small mirror (so you can look over the top of it) and put it vertically on a piece of paper. Looking in the mirror in one position, try drawing a dot behind the mirror where you "see" the spot. Because the mirror is small you should be able to see where your pen is pointing. Now shift where you stand (without moving mirror or ...


1

Absorption isn't an instant event. At the level of simple quantum mechanics, this system can be described as follows. Evolution of electron in crystal is governed by Schrödinger's equation. External electromagnetic field, namely the light which we shine on the crystal, is a periodic addition to the Hamiltonian. When you start shining light at the crystal, ...


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To calculate where an image is formed, you don't draw two parallel lines from the object to the lens (unless your object is at infinity). To see where a point on the object would for a point after the lens (hence forming an image) draw a line that goes parallel to the optical axis (and is refracted to go through the focus on the other side), and another that ...


1

When travelling in a dielectric light isn't light. It intracts with the medium to form a composite system that has an effective mass and therefore travels slower than $c$. If the interaction is strong, as in a BEC, the interacting system can be described as a quasiparticle called a polariton. This isn't useful for weakly interacting systems like most ...



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