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2

Yes, it is generally true. Imagine that your source is composed of many many point sources. Each point source produces a diffraction spot. The complete image is the sum of all of those spots. The points at the edge of an object will "spill" some intensity into the interior of the geometric image, but the diffracted intensity will "spill" outside of the ...


1

Both descriptions are correct; some people prefer the geometric description: the lattice of atoms is replace by a collection of planes, with different orientations. This corresponds to the Bragg model of partially reflective mirrors, and the K-vectors give the directions for the reflections which form the diffraction pattern. The description given by ...


3

The momentum of an electron, which is not travelling at very high velocity will not have any relativistic effects. So, its momentum is given by $$p=m_0v$$ where $m_0$ is the rest mass of electron ($9.1\times 10^{-31}~\rm kg$) and $v$ is the velocity. But to observe phenomena like diffraction (which observed with radiations like X-rays), the energy ...


8

Often, when dealing with high-energy (relativistic) particles the rest mass of the particle can be neglected when performing calculations. Use your expression for $p$ from relativistic considerations, plug in the numbers and see the negligible change when you include and neglect to include the mass of the electron. A good tip for when you enter into higher ...


3

The 4-momentum vector is given by ${\bf p}=(\frac{E}{c},p^{1},p^{2},p^{3})$. Now taking the scalar product with itself we have, \begin{equation} {\bf{p.p}}=E^2-(pc)^2=m_{0}^2c^4 \end{equation} Now for extremely relativistic case , we can use the condition that $E\gg m_0c^2$, thus this yields $p=\frac{E}{c}$.


8

As the energy of the electrons in that case is much greater than their mass, you can consider the approximation $E \sim pc$. So the formulas are equivalent.


0

The Abbe diffraction limit and the Rayleigh criterion (first zero in Bessel function) describe the same reality at the same level of abstraction. If optics are well-corrected for aberrations, we say they are diffraction limited, meaning that the geometrical and color aberrations are so small, that they don't matter in comparison to the diffraction limit ...


0

If they are calling the angles listed on the chart emission lines then I see eight all together. Starting with violet at an angle of 32.7 followed by 35.5, 33.1, 35.2, 42.4, 46.6 and 35.4. After reviewing I'm wondering now if it has more to do with the way the eight points blend together. 46.6 and 46.7 combine to make one line, 35.2, 35.4 and 35.5 combine ...


2

The following quote is relevant to whether in quantum mechanical terms there exists a monochromaticity possible , i.e. exact knowledge of momentum for the photon: instead of a slit, there is an electron. So the problem "photon impinging on slit" is a quantum mechanical problem, and there exists an uncertainty on the momentum of the impinging photon from ...


4

It seems to be still a research question for specific situations , but the answer is yes, gravitational waves diffract. example this paper: Emission of gravitational waves from binary systems in the galactic center and diffraction by star clusters From the abstract: The diffraction pattern of gravitational waves emitted by a binary system by a cluster ...


1

There's not necessarily uncertainty in the wavelength of the particle. The magnitude of the momentum vector could be the same for every particle, but its direction could be different. The particle's speed is certain, but the direction it heads in is not. In real light and particle sources, however, there is always uncertainty in the wavelength. Even lasers ...


0

Diffraction is bending (turning) around the corners. The turning is not possible without having slow speed at the edge, and faster speed around it. For gravitational waves, there is no known theory that says that GW speed changes through (or in proximity of) any matter. Therefore, no diffraction of gravitational waves. Even if diffraction is due to ...


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Diffraction can also occurr around abstruction . Suppose u put ur finger infront of light w.front such that ur fingers shadow will appear on the screen placed behind ur finger . When light w.front strikes ur finger then the light ray at the upper and lower extremes of obstruction will bend and enter in to shadow region generated by the obstruction and in ...



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