Diffraction refers to various phenomena that occur when a wave encounters an obstacle or opening. It is defined as the bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength, as shown in the inserted image. This is due to the addition, or interference, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the registering surface. However, if there are multiple, closely spaced openings, a complex pattern of varying intensity can result.
These effects also occur when a light wave travels through a medium with a varying refractive index, or when a sound wave travels through a medium with varying acoustic impedance – all waves diffract, including gravitational waves, water waves, and other electromagnetic waves such as X-rays and radio waves. Furthermore, quantum mechanics also demonstrates that matter possesses wave-like properties, and hence, undergoes diffraction (which is measurable at subatomic to molecular levels).
Homework Statement
1.compute the diffraction pattern through a ring aparture, internal radius a, external radius b, wave length lambda. the incoming wave is a monochromatic, plane wave, vertical to the ring plane.
2.how will the diffraction expression change when a->b?
3.near the aparture...
Homework Statement
Basically there's a question that I'm doing which asks me to show how to derive:
n lambda=d sin theta
We haven't learned it yet and so how do you do it?
Homework Equations
n lambda=d sin theta
The Attempt at a Solution
Not a clue!
Thanks!
When a photon diffracts through a slit, how long does it take to reach the farthest point of the diffraction pattern once it leaves the source? Would be it be the same as the time it takes to get from the source to the slit, plus to get from the slit to farthest point of light on the far wall...
Hello,
I need to calculate diffraction picture produced by source generating partially coherent illumination. I read Born and Wolf, Goodman and still I do not have complete understanding.
Suppose we have source with size d, simple object (let's take opaque rectangle) and detector. According...
In my Solid State course we've reached the topic of crystal diffraction and reciprocal lattices. I haven't had any problems so far, but I've hit a little snag in understanding how the diffraction condition 2\vec{k} \cdot \vec{G}=G^2 is equivalent to the Bragg law 2d\sin{\theta}=n\lambda.
In...
Okay, so I've been thinking about diffraction experiments and light, but not having a laboratory, I would like to know some specifics about what happens in a diffraction experiment. I know that laser light diffracts when it passed through a narrow aperture, but does it diffract as it passes out...
We all know, Bragg's law , n\lambda=2dsin\theta
where 2dsin\theta=path difference.
In the derivation of the path difference we take the two incident rays to be parallel which is perfect BUT we take reflected rays also to be parallel.How can this be since the reflected rays have to MEET for...
"When a wavefront of X-rays strikes an atom, the electrons in that atom interact with the X-rays and immediately re-emit the X-radiation, normally without change of wavelength, and the X-radiation that is emitted by the atom is emitted as a spherical wavefront "
Now my question is : visible...
Homework Statement
A diffraction grating of 3900 slits per centimeter is used to analyze the spectrum of mercury.
(a) Find the angular separation in the first-order spectrum of the two lines of wavelength 579 nm and 577 nm.
(b) How wide must the beam on the grating be for these lines to be...
I was just looking through Feynman's QED book (i'm surprised I'd never read it before) and I was wondering if anyone knew of any videos out there that actually experimentally demonstrate how light can be reflected by a diffraction grating even when the incident laser isn't actually POINTING at...
Hi guys,
I have a doublt about deducing the formula of dark fringe for single-slit diffraction. In the text, it reads "Consider two narrowstrips, one just below the top edge of the drawing of the slit and one at its center. The difference in path length to point P is (a/2)\sin\theta, where a...
I am reading texts on fundamental physics about diffraction and interference. When comes to diffraction, it takes a single slit as example and using Huygen's principle to explain how the wave transmitt and form the pattern. It sounds like that the pattern is due to interference. One textbook...
Homework Statement
What is the minimum thickness of coating which should be placed on a lens in order to minimize reflection of 661 nm light? The index of refraction of the coating material is 1.40 and the index of the glass is 1.65.
Hint: You must take into account the 180 degree...
Yesterday,our lab members discussed about the diffraction of incoherent beam.
I argued that if the beam is completely incoherent, it will not make diffraction patterns that
follows sinc or bessel-like function.
My argument is that the width of diffraction pattern is determined by light's...
Excuse me if this question is obvious.
Do mechanical waves propagate through loudspeaker diaphragms (whether they be elastic or rigid) in the same way that acoustic waves propagate through waveguides albeit a different medium? As far as I understand, reflections occur at the boundaries of the...
Hi! I know that x-rays interact with matter (compton effect). But I also know that when X-rays are incident on a crystal, they are diffracted following the Bragg's law.
My question is: why is the x-ray diffracted when it is incident on a crystal, but it isn't scattered by comtpon scattering?
1. In satisfying the Bragg's law, n\lambda=2d\sin\theta, n is typically assumed to be one, which explains why we see only one peak for a particular plane (say [400] plane for silicon). But I really don't see why n=2 should not appear as an equally strong peak..?
2. Is the Fourier transform...
Hi
I was just wondering if anyone knew a forumla for calculating the power intensity of waves, when diffracted through a circular aperture?
I have searched all over the net, but cannot find one which solves for the power intensity of the wave directly.
Homework Statement
Monochromatic light of 585 nm is shone on a slit of width 8.0 x 10^-2 mm and the interference pattern is produced on a screen 1.8 m from the source. What is the width of the first-order bright fringe?
Homework Equations
PD/w=x/L
The Attempt at a Solution...
Homework Statement
Monochromatic green light of wavelength
546 nm falls on a single slit with a width
of 0.095 mm. The slit is located 75 cm from
a screen. How wide will the central bright
band be?
Homework Equations
D sin 0dark = m 入
The Attempt at a Solution
Can...
Homework Statement
A single slit is illuminated with 630 nm light, and the resulting diffraction pattern is viewed on a screen 2.8 m away.
If the linear distance between the first and second dark fringes of the pattern is 12 cm, what is the width of the slit? Homework Equations
y=Ltan\theta
W =...
Homework Statement
The figure below shows an optical fiber in which a central plastic core of index of refraction n1 = 1.58 is surrounded by a plastic sheath of index of refraction n2 = 1.51. Light can travel along different paths within the central core, leading to different travel times...
Homework Statement
Can anyone explain to me how exactly this works because i thought that interference is supposed to oscillate up and down at the same height but in the "interference and diffraction combined" pattern, it's no longer the case...And also, I'm not sure but in the "interference...
A diffraction grating is labelled 300 lines mm^-1 (lines per mm)
Show that the spacing (d) between the lines on the grating is 3.3 x 10^-6m
i can't really think of any relevant equations. but I'm assuming standard form. i can't believe that the answer would be as simple as converting to...
Just another twist on the pinhole diffraction lab. This version of the experiment works great for kids to work in groups to make their own target if they are given a cheap red laser pointer and some very inexpensive easy to work with and SAFE materials. The objective is the determine the...
I want to find which elements and planes the intensity peaks in this graph comes from. The X-rays in the diffractometer are have a wavelength of 0.709 Å. The 2 \theta values for the peaks (including double peaks) are: 11.84, 19.56, 20.04, 23.28, 33.88 and 39.16.
Nickel, iron, silicon...
Homework Statement
The central bright fringe in a single slit diffraction pattern from light of wavelength 412 nm is 1.9 cm wide on a screen that is 1.05 m from the slit.
How wide is the slit?
Homework Equations
i keep trying the equation .5asintheta=.5wavelength
I can't seem to...
1. The distance between two slits is 0.0500 nm and the distance to the screen is 2.50 m. What is the spacing between the central bright fringe and the first-order fringe? Use yellow light with a wavelength of 580.0 nm. Answers: a. 0.010m b. 0.029m c. 0.290m d. 0.10m
e. 0.6m
2. y =LtanΘ...
Diffraction by a perfectly conducting cylinder using UTD?!
Hi all,
Does anybody know the equations needed to predict the diffraction of electromagnetic waves by a perfectly conducting cylinder using UTD?
I want to use these equations in ray tracing.
I tried to read some papers and a book...
Homework Statement
Hey guys, I'm working on a problem with a double slit electron diffraction experiment. There is a beam of electrons shooting through two slits onto a screen. When only slit 1 is open, the number of electrons hitting the screen is 25 times the number of electrons hitting...
I've been told that longer wavelengths are able to diffract more than short wavelengths. The hyperphysics page on sound wave diffraction also states this fact. Nothing I've read have explained why exactly longer wavelengths are able to diffract more than shorter wavelengths, so that's my...
Homework Statement
The interference pattern in this image:
http://session.masteringphysics.com/problemAsset/1074248/3/22.P45.jpg
is seen on a screen 1.0m behind an 950 lines/mm diffraction grating.
What is the wavelength of the light? (expressed in nanometers to 2 sig figs)
Homework...
Homework Statement
I'm having trouble solving this problem and I'm unsure why,
"A stereo speaker is located inside a speaker cabinet with an opening 30.9 cm wide. The speaker emits a sound with a frequency of 2620 Hz. Assuming that the speed of sound in air is 343 m/s, find the location...
Homework Statement
You wish to study a crystal's structure by diffracting thermal, non relativistic neutrons from the crystal, so you go to a nuclear reactor and set up your diffraction experiment on one of the neutron beam lines. The neutrons emerge from the reactor with a range of...
Homework Statement
Light of 650 nm can be seen in three orders in a particular grating. About how many slits per cm does this grating have?
Homework Equations
Yikes.
The Attempt at a Solution
Either this question is ridiculously hard resulting in me not even having a clue...
Homework Statement
A beam of yellow laser light (580 nm) passes through a circular aperture of diameter 4 mm. What is the angular width of the central diffraction maximum formed on a screen? (Define the angular width as the full angle from one minimum of the central diffraction maximum to...
hi again folks. this week's set of problems is getting my goat. here's another I can't seem to figure out.
Homework Statement
In a neutron two-slit diffraction experiment, the slits are 65 µm apart. If the third diffraction maximum is detected at an angle of 2 multiplied by 10-7 rad, what...
Hi!
I'm interested about this optical phenomenon but don't know how to explain why wavefront become more and more circularity when the slit is reduced?
http://www.shrani.si/?1Z/OG/2OhyYDXX/1/fizf0258.jpg
http://www.shrani.si/t/2k/wf/wMxtVum/1/fizf0260.jpg
diffraction grating URGENT
Homework Statement
A spectrometer is used to analyze a light source. The screen-to-grating distance is 50.0 cm and the grating has 5000 slits/cm. Spectral lines are observed at the following angles: 12.98, 19.0, 26.7, 40.6, 42.4, 63.9 and 77.6. How many different...
1. Homework Statement
a) Exactly 4 bright fringes are seen on either side of the central maximum when a diffraction grating is illuminated with yellow-green light of a wavelength of 570 nm. What is the maximum number of lines/meter for the grating?
2. Homework Equations
sin(theta) =...
Hi, i am new here, so am not really sure wheather i am asking this qus at the right place. I have a Lab based qus. I just did the atomic spetra analysis using a diffraction grating, analysing hydrogen gas.
But but when i calculate the wavelengths of the lines, its way off from the literature...
Bragg "diffraction" or "reflection"
As you read about X-ray (or neutron) diffraction in solids, you come across authors who use the term "Bragg diffraction" and others that use the term "Bragg reflection". Some authors even use both terms in the same edition of the book (Kittel, 5th Ed.,, I...
Homework Statement
On a crystal (cubic) a set of diffraction lines (θ) was obtained with CuKα (1.54 Å) radiation:
13.70, 15.89, 22.75, 26.91, 28.25, 33.15, 36.62, 37.60 and 41.95 degrees. Using
the following table to determine which peaks are expected to be absent in a cubic
P-, I-, and...
Homework Statement
Missing orders occur for a diffraction grating when a diffraction minimum coincides with an interference maximum. Let D be the width of each slit and d the separation of slits. (a) show that if d = 2D, all even orders (m=2,4,6) are missing. (b) show that there will be...
Homework Statement
A bulb emits a continuous spectrum of ultraviolet, visible and infrared light in the wavelength range 360nm to 2000nm. Assume that the light from this bulb is incident on a diffraction grating with slit spacing d and that the first-order brightness maximum for the wavelength...
Looking at diffraction gratings...
Ok, so I got a question in my assignment.
Monochromatic light of wavelength l is incident normally on a diffraction grating consisting of alternate opaque strips of width a and transparent strips of width b. The angle between the emerging zero order and...
Homework Statement
Coherent light is passed through two narrow slits whose separation is d. The second-order bright fringe in the interference pattern is located at an angle of theta.
If electrons are used instead of light, what must the kinetic energy of the electrons be if they are to...