Width Definition and 289 Threads

According to the formula, an increase in numerical aperture leads to a decrease in minimum line width and thus better resolution. However, if were to draw it out, given the same depth of focus, why does the minimum line width increase with higher numerical aperture?

hi, we have learned that after modelling Lagrangian and extracting Feynman rules from it - we can find matrix element - from which decay width can be calculated - and than Branching ratio - my question is can we use some other way of calculatiing BR , or can we use our Lagrangain in our Euler...

The New Measurement The ATLAS experiment at the Large Hadron Collider (LHC) has experimentally limited the "width" of the Standard Model Higgs boson with a rest mass of about 125 GeV to 4.5 + 3.3 - 2.5 MeV, with a maximum value of 10.5 MeV at a 95% confidence level. In the Standard Model, the...

Here is the solution, I understand how they got E, but I don’t see how they could get E’ from cosine addition formulas? I don’t need to know how to do it with complex numbers.

Greetings everyone, Exactly as the title says. I am reaching to something strange and I do not know what I am missing. It must be something obvious... case 1: -L/2 to L/2 After taking the Schrodinger equation and considering potential equal to zero inside we reach at this...

Hello there, I have derived the expressions for electric field and potential to be the ones above, then for continuity at ##x = 0## I set the electric fields and potentials to be equal to yield the expressions: $$Sx_p^2 = Kx_n^2$$ $$V_{bi} = V_n - V_p = \frac {q}{3\epsilon} \left( Sx_p^3 +...

Hi, I was working on this problem that I think should be quite simple, but I cannot seem to get the correct answer. Question: A pulsed laser operates at 850 nm wavelength. Under pulsed conditions there are several lasing modes present separated in frequency by ## \Delta f = c/2nl ## where...

I do not understand why that is the case. Is there any intuitive explanation for it? Thanks

How much does the equivalent width of a line change by the introduction of 5% scattered light? We know the equivalent width is defined as We know the equivalent width is defined as $$W = \int_{-\infty}^{\infty} \bigg(\frac{1-F_{\nu}}{F_c}\bigg) \, d\nu$$ where ##F_{\nu}## represents the flux in...

Monochromatic light is normally incident on a diffraction grating. The mth order line is at an angle of diffraction angle θ and has width w. A wide single slit is now placed in front of the grating and its width is then slowly reduced. As a result: A. both θ and w increase B. both θ and w...

i feel like subbing the numbers into the equation isn't enough because of the second minima and maxima thing? not sure what to do... would appreciate any help.

First, it is easy to see that n=4 after the collision because: E_1=-13.6\frac{1^2}{1^2}eV=-13.6eV E_4=-13.6\frac{1^2}{4^2}eV=-0.85eV E_5=-13.6\frac{z^2}{5^2}eV=-0.544eVBut, I never saw a definition for the width of an energy level. I tried to use something I saw online that said it was...

My attempt: 1) I am going to start this with a goal of setting up a reimann sum. First I divide the "arc"(?) of angle pi into n sub-arcs of equal angle Δθ 2) The total center of mass can be found if centers of mass of parts of the system are known. In each circular arc interval, I choose a...

Dear Physicsforum Mentors, For a pinion and gear wheel, the face width instead of 12mm for both, it should be 14mm and 12mm. The explanation I got is, when there's 0.2mm deviation in axial, then only 11.8mm width will be in meshing. later, when the system be worn out, that 0.2mm will be in...

My question for now is as follows: Why does a high doping concentration causes a decrease in the thickness of depletion region. Any help will be highly appreciated! Thanks a bunch Regards!

This is a diffraction grating problem I have been given that I am trying to answer Made a attempt at it and just wanted to see if I done this correctly or not? I get an angular width of 0.71 degrees which is very small Any help is much appreciated! Thanks

In these lecture notes about statistical mechanics, page ##10##, we can see the graph below. It represents the distribution (probability density function) of the kinetic energy ##E## (a random variable) of all the gas particles (i.e., ##E=\sum_{i}^{N} E_{i}##, where ##E_{i}## (also a random...

Hi all.I would like to know about "binning window". This paper I'm reading says like this. Why do "convolving the data with the ##b(t)## before the sampling" and "binning into time bins with a width ##δt##" have the same meaning? I know I'm addicted to post to PF 😅 But this forum is so...

In the process of trying to understand holography I encountered a detail that I kind of knew before, but just now I realized I have no idea how it works, how is it even possible. I’m talking about a simple pinhole camera where supposedly no matter how tiny a hole is a beam of light would still...

A container of height 3m and width 5m is filled with water upto 2 m. It is accelerated such that the water is at the brim (it is about to spill). When it moves with this acceleration find the force acting per unit width on the vertical wall. I found the acceleration for the condition provided...

Electron in atom at higher level(excited state) of energy has tendency jump to lower level of energy.Then the state of electron is unstale,so there is uncertainty in energy of the electron(the level of energy has a width).What cause the level being a band of energy but not a thin line of...

A new (short 3 pg) paper, making quite a grandiose claim, caught my eye last night: https://arxiv.org/abs/1908.07719 Abstract: We propose an experiment of two-path interference in which the optical path difference between the two interferometer arms is much larger than the spatial spread of...

The question is in the image. Working out with every step would be much appreciated.

If I am given the width of the slit (b), wavelength of the light (λ), and the distance of the slit from the screen (D), how can I find the width of the central maximum (d)? My book says d/2=Dλ/b, but with no explanation and I don't understand why. Where does this formula come from? Thank you...

I am working off the estimation that a simple beam of width w will be roughly half the strength of a beam of width 2w. (linear relationship, unlike beam depth). I am wondering if the cohesion of that beam matters tremendously (at practical scales), or if its width can be considered in a...

Homework Statement A strip of width w is a part of the plane bounded by two parallel lines at distance w. The width of a set ##X \subseteq \mathbb{R}^2## is the smallest width of a strip containing ##X##. Prove that a compact convex set of width ##1## contains a segment of length ##1## in every...

"Greg and Kristine are on opposite ends of a zip line that crosses a gorge. Greg went across the gorge first, and he's now on a ledge that's 15 m above the bottom of the gorge. Kristen is at the top of a cliff that is 72 m above the bottom of the gorge. Jon is on the ground at the bottom of the...

Homework Statement Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width? Homework Equations [/B] I solved for Ψ(x, t): $$\Psi(x,t) =...

When finding the fundamental for thin bars, the approximate equation (http://hyperphysics.phy-astr.gsu.edu/hbase/Music/barres.html) only refers to the length and thickness when calculating. I'm trying to figure out the frequency and node location along the length and width of the fundamental...

Homework Statement Calculate the ration of ##w_p/w_n## if n and p transistors in CMOS inverter necessary for the least delay time ##t_p## if the circuit is used in a chain of circuits. a) What is ##w_p## in that circuit if you're given : b) Calculate the maximum short circuit current if...

Homework Statement A laser emitting light with a wavelength of 560nm is directed at a single slit, producing an interference pattern on a screen 3.0m away. The central maximum is 5.0cm wide. 10mks Determine the width of the slit and the distance between adjacent maxima.[/B] Homework Equations...

Homework Statement Consider ultrasound with a frequency of 40 kHz. (a) What is the wavelength and period of a 40 kHz sound wave? (b) The slit width required to give the first order diffraction minimum at thirty degrees. (c) Calculate the angles at which the first three minimums should be...

I'm quite new to quantum mechanics. I have a question, I'm coding a small game with my friends and I do understand the orbitals and I've even written a function in java to simulate the probabilities of ONE of those diagrams, but I do not know my scale just yet, can anyone tell me the width of...

1. The problem statement, all variables and given/known Homework Equations ## \frac {PV1}{T1} = \frac {PV2}{T2} ## The Attempt at a Solution I find that v2 = 330/273 V1 But how can this related to the distance of P travel? Also, as the A gas pressed to B, i think the B gas try to resist. But...

1.A rectangular steelbar of length subjected to tensile force of 80kN. Calculate the change in length if the width and thickness are (40 & 25)mm respectively. (E = 207 GN/m2). Homework Equations E= stress/strain stress = F/A; F =80kN strain = dL/L 3. I just want to know what to use for the...

Homework Statement Determine the Full Width Half Maximum (FWHM) using the single coil equation and fitting parameters. The FWHM is the measure of how broad (wide) a signal is before it loses half of its intensity. In this case, its a measure of the distance spanned before the magnetic field...

How to calculate the width of spectrum produced by a dispersive prism of a given apex angle and refractive index, of white light of given width incident on first face of prism?

I was wondering that we always see the diameter of milky way but no one talks about its width. Even on google it is not there. This means that if I go up instead of forward then I would be out of milky in an instant?

Hi guys, I am learning for an optics examination and found a picture that is supposed to show the duration of a light pulse with respect to the spectral bandwidth (appended). At this point in the lecture, we have not gone through modelocking yet, so I assume one should understand the picture...

Homework Statement Homework EquationsThe Attempt at a Solution LCR circuit, calculating R when frequency width is given Applying Kirchoff Voltage Loop Law, ## V_A – V_B + V_B - V_C + V_C – V_A = 0 ## ...(2) ## V_A – V_B ## is potential drop across inductor. Since current is flowing...

Homework Statement Homework EquationsThe Attempt at a Solution When the system is in air ## d \sin {\theta} = n \lambda ## ...(1) When the system is in water and slit separation is 2d, ## \mu 2d \sin {\theta} = n \lambda ## ...(2) ## \tan {\theta} = \frac y D ## ...( 3)...

Homework Statement Homework EquationsThe Attempt at a Solution I think before getting the steady state, after doping there are more electrons in n-region and there are more holes in p-region, so the more electrons go towards the p-region and more holes go toward the n - region. Consequently...

Homework Statement Homework EquationsThe Attempt at a Solution The answer is no as it is not dimensionally correct. Right?

Hello, I've been researching photovoltaics and I've seen some articles which state that the width of the depletion layer is not equal on both sides on the pn junction. i don't understand why this occurs I've tried to research why and how this happens but have been unable to find an answer.

I have a question that I feel I cannot find enough on. We just did a practical in Physics class where we used a laser light shined on a single hair strand in order to create a diffraction pattern and use formulae to determine the hair's width. Because of Babinet's principle, the hair managed to...

In an unbiased p-n junction, how does increase in doping affect the width of Depletion Region? I read somewhere that width decreases as increase in carrier concentration leads to more recombination of majority carriers with oppositely charged ions of their depletion regions leading to a...

Here is what I want to know specifically: if I replace my 5cm wide rear tire with a 6.25cm wide tire, how much can I increase the inflation pressure to obtain the same comfort? I realize "comfort" is not a quantifiable measurement, maybe shock absorption characteristics is better. Perhaps it...

Homework Statement A particle of mass m is moving in an infinite square well of width a. It has the following normalised energy eigenfunctions: $$u_n (x) = \sqrt{\frac{2}{a}} sin(\frac{n \pi x}{a})$$ (1) a) Give an expression that relates two orthogonal eigenfunctions to each other and use it...

Hello Physics Forums I’m doing some numerical studies on diffusion. I began with monte carlo simulations on gas diffusion, and more recently I’ve started to dabble in carrier diffusion inside semiconductors. It looks like diffusion in semiconductors is a lot more amenable to experimental study...

Hi all, I'm studying ## \mu \to e~ \gamma ## decay from cheng & Lie' book " gauge theory of elementary particles ". In Equation (13.84), he wrote the neutrino propagator ## \sum_i \Big ( \frac{U^{*}_{ei} U_{\mu i}}{(p+k)^2-m_i^2} \Big), ## (where the sum taken over neutrinos flavors) in the...