# 0.4 2d and 3d wavefronts  (Page 5/7)

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A slit with a width of 2511 nm has green light of wavelength 532 nm impinge on it. The diffracted light interferers on a surface, at what angle will the first minimum be?

1. We know that we are dealing with interference patterns from the diffraction of light passing through a slit. The slit has a width of 2511 nm which is $2511×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ and we know that the wavelength of the light is 532 nm which is $532×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ . We are looking to determine the angle to first minimum so we know that $m=1$ .

2. We know that there is a relationship between the slit width, wavelength and interference minimum angles:

$sin\theta =\frac{m\lambda }{a}$

We can use this relationship to find the angle to the minimum by substituting what we know and solving for the angle.

3. $\begin{array}{ccc}\hfill sin\theta & =& \frac{532×{10}^{-9}\mathrm{m}}{2511×{10}^{-9}\mathrm{m}}\hfill \\ \hfill sin\theta & =& \frac{532}{2511}\hfill \\ \hfill sin\theta & =& 0.211867782\hfill \\ \hfill \theta & =& {sin}^{-1}0.211867782\hfill \\ \hfill \theta & =& 12.{2}^{o}\hfill \end{array}$

The first minimum is at 12.2 degrees from the centre peak.

From the formula $sin\theta =\frac{m\lambda }{a}$ you can see that a smaller wavelength for the same slit results in a smaller angle to the interference minimum. This is something you just saw in the two worked examples. Do a sanity check, go back and see if the answer makes sense. Ask yourself which light had the longer wavelength, which light had the larger angle and what do you expect for longer wavelengths from the formula.

A slit has a width which is unknown and has green light of wavelength 532 nm impinge on it. The diffracted light interferers on a surface, and the first minimum is measure at an angle of 20.77 degrees?

1. We know that we are dealing with interference patterns from the diffraction of light passing through a slit. We know that the wavelength of the light is 532 nm which is $532×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ . We know the angle to first minimum so we know that $m=1$ and $\theta =20.{77}^{\mathrm{o}}$ .

2. We know that there is a relationship between the slit width, wavelength and interference minimum angles:

$sin\theta =\frac{m\lambda }{a}$

We can use this relationship to find the width by substituting what we know and solving for the width.

3. $\begin{array}{ccc}\hfill sin\theta & =& \frac{532×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}}{a}\hfill \\ \hfill sin20.{77}^{o}& =& \frac{532×{10}^{-9}}{a}\hfill \\ \hfill a& =& \frac{532×{10}^{-9}}{0.354666667}\hfill \\ \hfill a& =& 1500×{10}^{-9}\hfill \\ \hfill a& =& 1500\phantom{\rule{4pt}{0ex}}\mathrm{nm}\hfill \end{array}$

The slit width is 1500 nm.

run demo

## Shock waves and sonic booms

Now we know that the waves move away from the source at the speed of sound. What happens if the source moves at the same time as emitting sounds? Once a sound wave has been emitted it is no longer connected to the source so if the source moves it doesn't change the way the sound wave is propagating through the medium. This means a source can actually catch up to the sound waves it has emitted.

The speed of sound is very fast in air, about $340\phantom{\rule{4pt}{0ex}}{\mathrm{m}·\mathrm{s}}^{-1}$ , so if we want to talk about a source catching up to sound waves then the source has to be able to move very fast. A good source of sound waves to discuss is a jet aircraft. Fighter jets can move very fast and they are very noisy so they are a good source of sound for our discussion. Here are the speeds for a selection of aircraft that can fly faster than the speed of sound.

 Aircraft speed at altitude ( ${\mathrm{km}·\mathrm{h}}^{-1}$ ) speed at altitude ( ${\mathrm{m}·\mathrm{s}}^{-1}$ ) Concorde 2 330 647 Gripen 2 410 669 Mirage F1 2 573 715 Mig 27 1 885 524 F 15 2 660 739 F 16 2 414 671

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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