# 0.4 2d and 3d wavefronts  (Page 4/7)

 Page 4 / 7

## Diffraction through a slit

When a wave strikes a barrier with a hole only part of the wave can move through the hole. If the hole is similar in size to the wavelength of the wave then diffraction occurs. The waves that come through the hole no longer looks like a straight wave front. It bends around the edges of the hole. If the hole is small enough it acts like a point source of circular waves.

Now if we allow the wavefront to impinge on a barrier with a hole in it, then only the points on the wavefront that move into the hole can continue emitting forward moving waves - but because a lot of the wavefront has been removed, the points on the edges of the hole emit waves that bend round the edges.

If you employ Huygens' principle you can see the effect is that the wavefronts are no longer straight lines.

Each point of the slit acts like a point source. If we think about the two point sources on the edges of the slit and call them A and B then we can go back to the diagram we had earlier but with some parts blocked by the wall.

If this diagram were showing sound waves then the sound would be louder (constructive interference) in some places and quieter (destructive interference) in others. You can start to see that there will be a pattern (interference pattern) to the louder and quieter places. If we were studying light waves then the light would be brighter in some places than others depending on the interference.

The intensity (how bright or loud) of the interference pattern for a single narrow slit looks like this:

The picture above shows how the waves add together to form the interference pattern. The peaks correspond to places where the waves are adding most intensely and the minima are places where destructive interference is taking place. When looking at interference patterns from light the spectrum looks like:

There is a formula we can use to determine where the peaks and minima are in the interference spectrum. There will be more than one minimum. There are the same number of minima on either side of the central peak and the distances from the first one on each side are the same to the peak. The distances to the peak from the second minimum on each side is also the same, in fact the two sides are mirror images of each other. We label the first minimum that corresponds to a positive angle from the centre as $m=1$ and the first on the other side (a negative angle from the centre) as $m=-1$ , the second set of minima are labelled $m=2$ and $m=-2$ etc.

The equation for the angle at which the minima occur is given in the definition below:

Interference Minima

The angle at which the minima in the interference spectrum occur is:

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

where

$\theta$ is the angle to the minimum

$a$ is the width of the slit

$\lambda$ is the wavelength of the impinging wavefronts

$m$ is the order of the mimimum, $m=±1,±2,±3,...$

A slit with a width of 2511 nm has red light of wavelength 650 nm impinge on it. The diffracted light interferes on a surface. At which 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 650 nm which is $650×{10}^{-9}\phantom{\rule{4pt}{0ex}}\mathrm{m}$ . 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. $\begin{array}{ccc}\hfill sin\theta & =& \frac{650×{10}^{-9}\mathrm{m}}{2511×{10}^{-9}\mathrm{m}}\hfill \\ \hfill sin\theta & =& \frac{650}{2511}\hfill \\ \hfill sin\theta & =& 0.258861012\hfill \\ \hfill \theta & =& {sin}^{-1}0.258861012\hfill \\ \hfill \theta & =& {15}^{o}\hfill \end{array}$

The first minimum is at 15 degrees from the centre peak.

What is population studies?
What are the subjective reality of mass communications
preconditions that give rise to deviance behavior
what do you mean by "power to constraint"?
can someone please elaborate the main elements of ethnicity.
Tinya
What is social thought? And the difference between social thought and sociological thought
Please some one should explain this theories for me.. Functionalism,, conflict theory and symbolic interaction
functionalism: interrelated parts designed to meet the biological and social needs of the individuals in that Society
Lisa
conflict Theory: the way inequalities contribute to social differences and perpetuate difference in power
Lisa
Symbolic: one to one interactions and communications
Lisa
Can this theories be criticise?
onoja
what is Karl max.
karl Marx is a economist and he worked in sociology he proposed theory of communism
Zakir
communism said that Every member of society acquired equal rights means equal basic needs of life ...he said capitalism gain all the profits and worker remain in same situation they can't effort even his three times meals in a day
Zakir
What are the main tasks of Sociologist
Does a full Moon really trigger strange beh
please does anyone doing Anthropology here. I need help on the notes
my course is a combination of sociology and anthropology. please I need some notes
Pascal
Actually am doing sociology
Abubakar
mmm ok I have a friend of mine who is offering Anthropology perhaps I will talk to him about the notes
Abubakar
where from u
BILAL
yuusuf
Any body define Global implications nd technology
BILAL
hi
Elias
what are the differences and similarities between August Comte and Herbert Spencer theories? pls I need some response on that.
Elias
Hyy
BILAL
hello
Pascal
hello
roamers
good morning from here
Pascal
morning
ram
good Morning
shoaib
please is there any way someone can have a private message here
Pascal
hii
fazil
hello
Pascal
hii
fazil
good morning pascal
fazil
hii
fazil
gd morning ram
fazil
plz try to answer the question above. don't say hi, helo and so on
yuusuf
Mr/Ms pascal there is no other option to have private massage here. try onother option to get private massages from here
yuusuf
trying to answer the advantage and disadvantage of multiculruralism. 1. The advantage is multethnic countries are home to majority of migrants a signifacant population of it being a highly educated skilled of workforces aroun the world.
yuusuf
2. Disadvantage may couse risk of social conflict occurs due to differences in relegios, beliefs, and practoces though ethnic retuals or certain weys of life that may couse rift between two or more groups.
yuusuf
more result plz References (Opinionfront.com)
yuusuf
How would you classify crimes like child abuse, human trafficking and domestic violence?
I would say that these are very serious crimes especially because they hinge on the rights of human beings, therefore they would be classified as felonies. Felonies;are the most serious of crimes that one can commit.
Douglas
what are the factors responsible for drug addiction using the theories of deviance
parents are the first responsible for drugs addiction in our society today
Yakubu
what are the unique features of rural areas?
Got questions? Join the online conversation and get instant answers!