diffractioninterferenceopticswaves
My book says :
The number of interference fringes occuring in the broad diffraction peak depends on the ratio d/a that is the ratio of the distance between the two slits to the width of a slit. In the limit of "a" becoming very small, the diffraction pattern will become very flat and we will observe the two slit interference pattern.
How can interference pattern be observed in a diffraction pattern? Why does it depend upon the ratio d/a? Why will we observe interference when a is very small?
According to the Huygens–Fresnel principle, every point of the wavefront is a new spherical wave source. Of course, you don't see infinite individual waves; what you see is the result of summing (interference) infinite waves.
This means there is always interference, even if there are no obstacles. Diffraction would be a consequence of blocking part of the wavefront, so the waves which are left interfere in some fancy way. This principle can be used to describe refection, refraction and diffraction.
For a single slit several times bigger than the wavelength (the dots are the wave sources):
If the slit is as big as the wavelength you see a single spherical wave (I wouldn't be sure to consider this diffraction at all):
There is something similar to the Huygens–Fresnel principle in quantum electrodynamics. The path integral formulation says that when light (and any other particle) travels to a point $A$ to a point $B$, you have to sum every possible trajectory. Each trajectory has the same probability, they only differ in phase.
So for the two slit, if you compute each possible path you would get the classical result.
So I would say that diffraction is a particular case of interference where some part of the wavefront has been blocked.
But the difference between interference and diffraction is not clear. As Feynman said: "no-one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them".
Fringe is some sort of rectangle not a point. we can talk about distance between two points not distance between two say, bands.
I'm not sure what your question is. However, your statements are examples of loose but commonplace language. It would be more accurate to say the shortest distance between adjacent bands, or the spacing between bands.
I think both interference and diffraction fringes are equal width - determined by wavelength, distance between slits and screen and distance between slits or width of one slit.
The geometry of the fringes are determined by all of the variables you've determined. That doesn't mean that the expressions have to be equal. For example, the two expressions $at$ and $at/2$ both depend on $a$ and $t$, but they don't yield the same result.
in one text book - it is mentioned that in diffraction fringe widths are not same where it is same in interference. Is it right?
If click this Google image search, you'll see the closely spaced interference fringes and the wider spaced diffraction envelope. Using a ruler or your fingers, you may be able to answer this question by directly measuring.
If you'd like more info, this link has some more details on both types of fringes.
Best Answer
Interference is the sum (even with negative sign) of energy or impulse of two water or sound waves at a given point. For photons this could not be applied since photons do not interact with each other at the energy level of our usual used light sources.
If, and only if, one agree that light is a stream of photons, the phenomenon of interference is not applicable to the intensity distribution behind edges. If one use the imagination of light as a waves this lead to an other complication. Youngs sketches, showing the interference pattern of water waves , are "frozen" pictures of moving patterns of interference maxima and minima. In our time of animated sketches (or videos) this can be seen clearly.
Furthermore one can show, that the photons get influenced at sharpe edges and than spread out in such a way that they form stationary intensity patterns on an observation screen. The influence happens between the surface electrons - their electric field is concentrated on sharpe edges - and the electric field component of the photons. This point of view allows to explain even single photon experiments and even with a single edge instead of a slit or multi slits.
Last not least it has to be explained, how the EM waves get in phase at the edge. The non mainstream answer is, that the surface electrons of the edge(s) and the electric field component of light influence a common field and this quantized field deflect the light into intensity distributions. The pattern of this distribution is an image of the quantized field around the edge.
I'm here to learn and it would be nice to get responses around the first step, where I'm violating the description of physical processes.