You need to know somethings in superposition. It is a highly general term and so there is no thing called constructive and destructive superposition
The idea is very simple, when two waves meet they form a resultant wave, the waves do not need to be coherent and identical in frequency. The resultant wave formed can be larger than the individual waves or smaller. Either one has no specific term.
You will need to know how to draw the resultant wave
When they give two waves, they each have a displacement at a particular point - either positive or negative or same.
At different points, take the sum of the displacements of the two wave at that particular time like above and so plot the resultant wave points
When you have enough points, draw the smooth wave curve
Interference is a highly specific category under superposition which deals with only coherent waves and has specific terms when the maximum resultant and the minimum resultant is formed.
So as we know what are coherent waves, we will talk about the specific terms of interference, but before that we need to know what's out of phase and in phase
It always is 180° and so it is a specific term or difference. At this point, the waves fully cancel out each other in the maximum way as possible, resulting in the lowest resultant wave displacement
It always is 360° and so it is a specific point or difference. At this point, the waves fully joins together in the maximum way possible, resulting in the Highest resultant wave displacement
It is not truly destructive or constructive. However, we just need to know the two specific angles in which the maximum and the lowest resultant is formed
As mentioned, phase difference increases every 360°, which means the destructive interference at 180° is also the same as 540°. The phase difference of 360° is same as 0° and also the same as 720° and so on
Also waves do not have to be the same amplitude but, must have the same frequency (coherent).
Lastly, this point is quite important:
Remember interference pattern must have both maxima and minimas
So an interference pattern must have both to identify it is a pattern
Usually when doing experiments we need to have two or more source which produce coherent waves so they can interfere
This is done by using a single wave source behind a barrier which has two or more gaps and when the waves pass through the gaps they diffract and curve but, they still have the same frequency or wavelengths. So then they can interfere to produce an interference pattern
So they have curved waves which has the same wavelengths as before
There is an important point you need to remember:
However in MCQs, it is more trickier as they state that the diffraction angle ( amount of diffraction ) increases when the gap width decrease until it is optimum when the gap is equal to the wavelength
But if the gap width is greater than the wavelength, the amount of diffraction is less, so if you decrease the wavelength and keep the gap width constant, the diffraction angle decreases
The point where they interfere contructively, they produce a maxima or a bright fringe. Points where they interfere destructively, they produce a minima or a dark or weak fringe
But how to calculate if the waves are interfering constuctively or destructively, We need the idea of path difference!
So what is the diffraction angle, We know as waves spread the direction of the wave energy spreads, and so the angle between these direction of the wave energy is called diffraction angle.
Greater the diffraction, greater the angle
This principle is used in microwaves. So as microwaves have a wavlength in cm, the gaps in the grills of the microwave are quite small. This do diffract the waves but the wave power doesn't pass that much. In order words, the wave is reflected back
So why do we find the difference in length. This actually shows whether a wave is ahead of each other or not. Also to see if they meet at a crest or a through
So we get the path difference in meters
After that, if the path difference is not zero, it shows that one wave is ahead of the other. But by how much? Half a wave, a wave or 2 waves...
We know wavelength is the distance of one complete wave so when the path difference is divided by wavelength, it shows how many wavelengths or waves ( in terms of a number ) the waves are apart
This experiment is useful in finding the wavelength of a wave source
a - is the seperation of the slits
x- is the seperations between two nearest bright fringes or dark fringes
There is an important part:
The distance between two nearest fringes(dark or bright) are always x and remains the same.
Distances between a dark fringe(minima) and the bright fringe(maxima) is half of x and it also remains constant anywhere
So to find x we may need to multiply the distance between a maxima and minima by 2
It doesn't really matter which is a or x. Just keep each consistent
So this is used in experiments to find the wavelength of a light source. The two light sources must be coherent.
When we we have more than two slit, we get a inteference pattern. However, the maximas are more spaced out and more sharp!
So d is actually the slit seperation and because it very small, it is found by a method
The angle θ is the angle from the order to the central maxima
The n has a special meaning in diffraction grating:
The central maxima is called Zeroth order maxima or 0th order maxima
So the nth number increases each time there is a maxima
So the equation above gives the angle of the order from the Zeroth order maxima
There are some important points you need to remember
So angles to the zeroth order on one side is same as the angles on the other side. So it is symmetrical in the zeroth order plane
So the angle between the two 2nd orders is the twice as the angle from the 2nd order to the zeroth order
This is an important point! In fact the distance between the maximas are not the same and also the angles between them are not the same.
If you need to find the angle between two maximas. First, find the larger angle to the zeroth order and minus the smaller angle to the zeroth order
So find the angle when n is 2
So find the angle when n is 1
So this is the angle between the first order and the second order
This is actually known as the slit seperation or grating spacing or slit spacing
There is a common misconception that d is the slit width, but this is wrong. It is actually the seperations between the slits. So its similar to the young double slit experiment. However, as the slit seperation is very small, we use the term slit spacing instead.
They usually give the number of line/slits per mm or meter
So for example, if they say 600 lines per mm
We divide by 1000 to convert it to meters
We have only looked at single wavelength questions but, white light contains a variety of wavelengths. When the white light passes through the slits, the light splits into many colors. This is called dispersion.
So each wavelength of light would have its own maxima on the screen
The variety of colors can only be seen in a diffraction grating and not in a young double slit because the maximas are more far apart
Now you need to remember that the central maxima is always a white maxima. This because for any wavelength of light it always meets at the center, so this would anyways produce a white light.
So shorter wavelengths such as violet will have a smaller angle according to this equation
So when the wavelength is greater(red) the angle is greater
So it will be white in the center then violet closest to the center and then red furthest away
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