Optics : interference and diffraction

[Abishek Balaji]

interference is a superposition of two waves coming two slits...
diffraction is a superposition of a family of waves from a single slit..
then how the fringes formed during double slit experiment is actually a superposition of single-slit diffraction from each slit and the double-slit interference pattern ??
I read
"the broader diffraction peak is actually made of several fringes of smaller width due to double-slit interference and the number of interference fringes occurring in the broad diffraction peak depends on the ratio of the distance between the two slits to the width of a slit. in the limit of the width of the slit becoming very small, the interference pattern will become very flat and we will observe two slit interference pattern..."
somebody please explain... I'm finding optics difficult to grasp... thanks in advance...

 

[Alfred Cann]

In the 2 slit experiment, the slits must be narrow enough to make the main lobes of their diffraction patterns wide enough to overlap. Only in this overlap region will there be light from both slits, so that interference can occur.
The book you quote sounds overly laconic; no wonder it is hard to understand. Perhaps this section refers to an earlier section of the book where a wide slit is modeled as a superposition of many pairs of slits? Not helpful.

 

[blue_leaf77]

diffraction is a superposition of a family of waves from a single slit..

This is a common misconception about the difference between interference and diffraction. Diffraction is the change of the field (or disturbance, to include any kind of waves) distribution in space due to the passage of the wave through a hindrance, some examples of which are slits and lens. So, the focusing or diverging of light is also an example of diffraction. This change of field distribution after passing through a hindrance is made possible by the waves being able to interfere. Had the nature been constructed such that lightwave knows nothing about interference, we wouldn't probably have seen the diffraction from a slit the way we do today.

then how the fringes formed during double slit experiment is actually a superposition of single-slit diffraction from each slit and the double-slit interference pattern ??

I would refrain from using the word "superposition" to describe the intertwining between the single slit diffraction pattern and the double slit interference pattern in the mathematical form of the double slit diffraction pattern because the two patterns are multiplied in the formula, not added.

"the broader diffraction peak is actually made of several fringes of smaller width due to double-slit interference and the number of interference fringes occurring in the broad diffraction peak depends on the ratio of the distance between the two slits to the width of a slit. in the limit of the width of the slit becoming very small, the interference pattern will become very flat and we will observe two slit interference pattern..."
somebody please explain... I'm finding optics difficult to grasp... thanks in advance...

Does your source not provide the mathematical treatment of the problem? Every field of physics will be identically difficult to grasp if one only rely on mere paragraphs, the complete message of a physics problem is conveyed along with the maths.

 

[lychette]

interference is a superposition of two waves coming two slits...
diffraction is a superposition of a family of waves from a single slit..
then how the fringes formed during double slit experiment is actually a superposition of single-slit diffraction from each slit and the double-slit interference pattern ??
I read
"the broader diffraction peak is actually made of several fringes of smaller width due to double-slit interference and the number of interference fringes occurring in the broad diffraction peak depends on the ratio of the distance between the two slits to the width of a slit. in the limit of the width of the slit becoming very small, the interference pattern will become very flat and we will observe two slit interference pattern..."
somebody please explain... I'm finding optics difficult to grasp... thanks in advance...

The description in your book is OK. A single slit produces a DIFFRACTION pattern with a broad central maximum and (subsidiary) maxima on each side.
The width of the central maximum depends on the width of the slit.
Whe the 2 DIFFRACTION patterns from 2 slits combine INTERFERENCE will occur where the single slit maxima overlap. The interference patter consists of maxima and minima with spacing determined by the SEPARATION of the slits.
I would describe the interference pattern as being contained within the DIFFRACTION 'envelope' of the slits.

 

[sophiecentaur]

Splitting the problem up into two parts is a big help in the calculation. When all the apertures are identical and oriented in the same way, you have 'separable variables' and the Interference pattern from ideal point sources (based on ∑ calculations) can be multiplied by the Diffraction pattern of one aperture (based on ∫ calculations). It doesn't matter which order you do the calculation for a particular angle; it is a commutative process.
You can only do this for identical apertures. If the individual apertures are not the same then you have to work out the Integral over the whole source of the waves (as when you calculating the hologram pattern formed from a group of irregular objects).
In practice, you can use your common sense and 'ignore' the individual slit diffraction pattern if the slits are significantly narrower than the spacing, to calculate the pattern near the central axis.

 

[lychette]

In the 2 slit experiment, the slits must be narrow enough to make the main lobes of their diffraction patterns wide enough to overlap. Only in this overlap region will there be light from both slits, so that interference can occur.
The book you quote sounds overly laconic; no wonder it is hard to understand. Perhaps this section refers to an earlier section of the book where a wide slit is modeled as a superposition of many pairs of slits? Not helpful.

I will attempt to post a sketch showing the relationship between the interference pattern of 2 slits and the diffraction (envelope) of a single slit...hope it helps.
I am surprised that there is not a sketch of this sort in your textbook to make the point clear.