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## Physics library

### Course: Physics library>Unit 14

Lesson 2: Interference of electromagnetic waves

# Single slit interference

What happens when there's only one hole? Created by David SantoPietro.

## Want to join the conversation?

• what happens when you combine the concepts of single slit and double slit together? why cant you see the single slit pattern in double slit interference?
• that is such a cool question.

The answer is that you do see it. Its a little difficult to explain face to face even, so on here, may be a bit tough, but, here goes...

start with a single slit pattern. looks like a big hill in the middle with smaller hills on each side ok??

http://www.clemson.edu/ces/phoenix/labs/224/diffraction/fringes.jpg

The look at double slit. lots of equally sized hills (max) and valleys. (Min)OK so far??

http://images.fineartamerica.com/images-medium-large/1-double-slit-diffraction-pattern-omikron.jpg

So, where is the single slit pattern in the doubles slit pattern??

Well, if you look again at the double slit patter, the hills are not all he same size. They get smaller as you move away from the centre line. Now, how quickly they get smaller depends upon the size of the individual single slits that make up the double slit.
As the slits of the double slit arrangement get narrower, what happens to the double slit pattern? You will see that if the slits are very narrow, then the hills (maxima) in the double slit pattern get smaller but much slower.
One way to say it is this....
The interaciton of the light from the two slits produces the regular max-min pattern
The size of the individual slits determines the shape of the 'envelope' that controls the size of each of the maxima. Let me see if I can find a diagram to help...

OK; This is pretty good
http://physics.stackexchange.com/questions/109243/why-are-there-interference-patterns-inside-a-diffraction-envelope

hope that helps...if not, shout

But its a great question; shows good thinking
• How come pairing the top point and 5th point from the top produces a distance of w/2 ? There are 4 inter-point intervals between those two points but only 3 inter-point intervals among the rest of the points. So it didn't divide the slit into half.
• Sorry for any confusion. Yeah, using just eight sources was a way to get the idea across. When the number of sources N is allowed to be infinite (or very, very large), the distance between the first source and N/2 + 1 source will approach w/2. I wanted to keep the number of sources even so we could pair each source in groups of two with none left over. Although, I suppose when the energy of the wave is distributed over infinitely many sources, having one infinitesimal source left over doesn't really matter anyways.
• What is the difference between interference and diffraction?
• Diffraction occurs when light bends around an obstacle. When light diffracts, it will create an interference pattern since the waves will no longer all be in phase from the coherent light source. Essentially the diffraction causes the interference to occur.
• are you sure it is the same angle?
• Yes, The angle measured in the video is correct.
(1 vote)
• By using the distance w/2 we find the θ of the first destructive interference. But, when we use a different distance (w/5, for example), a different value of θ can be found, which isn't necessarily multiple of the first one! Why does that happen?
• Below is my understanding, and someone can correct me if I'm mistaken:

At , David says that IF the top and middle beams of light interfere destructively, then all of the other beams of light will interfere destructively (as every beam of light will have a "partner" that destructively interferes and thus cancels it out).

In other words, in cases where the beams of light at the top and midpoint are destructive, then we will see this diffraction pattern. This will occur when the difference between the lengths of the beams of light are (lambda)/2.

For other cases, the diffraction pattern will be less noticeable, or non-existent. Consider how we do not observe diffraction patterns when there are larger holes in, say, window curtains. These diffraction patterns occur under the assumption that the slit is small relative to the wavelength of the light - i.e. w<(lambda).

Again, this is my understanding, as I was also confused by this and couldn't find a clear explanation on the internet.

Additional note: for w>(lambda), see the next video, titled "More on single slit interference".
• Why is w/2 chosen as the distance? Why not w/3?
• If you choose w/2, you can pair every point with another. If you choose w/3 you'll have a third of all the points left over
• Thanks Teacher Mackenzie! For some reasons I cant press the comment button, so I'll just post my question again here.

Is it correct to say that double slit pattern is the sum of 2 single slit patterns combined together?
If that is correct, then two slits that are very close will form a single slit pattern, and two slits that are very far apart will form two single slit patterns.
• no; sorry to say that is not the case. The double slit pattern is not a combination of two singles slit patterns.
But you can see BOTH patterns at the same time.
For the double slit pattern, The waves from each slit 'combine' to form the regular maxima and minima of the double slit pattern. Here
http://images.fineartamerica.com/images-medium-large/1-double-slit-diffraction-pattern-omikron.jpg

But you can see here that each of the slits has its own 'influence' on the pattern of maxima and minima.

Here is a rough explanation:
Imagine if we have two identical sound sources A and B. and combined, they produced a new sound C.
The new sound C is due to the interaction of A and B.
But then we find that A has its own independent effect on C
And B also has its own independent effect on C
So there are two effects going on here... the COMBINED effect of A and B
and the independent effects due to A and the effect due to B.

So thats what is happening here.

See the green picture above....The combination of the two coherent sources produces the regular max/ min pattern of a double slit diffraction pattern. But look, it is gradually fading towards the edges...that is the effect of the single slit pattern.
So the individual slits 'superimpose' their individual effects ONTO the double slit pattern. We say that the individual slits have imposed a single slit 'envelope' onto the double slit pattern

looks like this

hope that is clear.... not an easy concept to grasp, so please keep asking f its not making sense yet...
• Why must the width between the two paths be w/2 for them to destructively interfere as demonstrated at ?
• if width of slit is made double , how does it affect size and intensity of central diffraction band ?
• Ok so, initially the equation is dsin(t) = m L/2 (t being theta, L being lambda). Unlike the double slit experiment, the d (the distance between two sources of wavefronts) can be varied. So theoretically I can pick any random point on the final screen, measure it's angle, t, from the point source being analyzed, and then pick a different point source that is a correct distance, d, from the original point source to destructively interfere with it at the final point on the screen. Basically, wouldn't it be true that for every point on the final screen, there will be two point sources that destructively interfere? And then using the logic of this video, couldn't i justify pairing up all the other points with their respective points of destructive interference? Obviously this isn't true, because then there would be no interference pattern at all, but what am i missing here? Why isn't this true?

The decision to pick d = w/2 just seems so arbitrary to me. Why would the half-way point guarantee destructive interference?