mehul mahajan said:I'm finding problem understanding your question, what i know is that the path difference = d sinθ
and for constructive interference d sinθ =n λ
where n is an integer.
terryds said:In Young's double slit formula, the equation is
d sin \theta = m \lambda
Which means that
sin \theta = m \lambda / d
But, what if d < \lamda so the sine value becomes greater than 1?
Will there be any interference?
sophiecentaur said:If d is small, there will be no total cancellation but interference will still cause a drop in the amplitude as the angle increases.
It is valid because it only describes the positions of zeros and there is no zero for closely spaced slits.terryds said:So, does the formula still valid for d < lambda?
If the slits are too close together, the phase difference between the waves from the two sources can't be as great as π and so you can't have complete cancellation at 90°. Nevertheless, if there is a reflex angle between the two E vectors, the resulting amplitude will be noticeably lower than where they add and you will get a minimum but the zero is, as you say, at an invalid angle for the formula. I tried a brief search for a suitable diagram of the patterns of two omnidirectional sources on Google but I could find nothing. It's the sort of picture you get in books on antenna theory.terryds said:Why will there be no total cancellation?
sophiecentaur said:It is valid because it only describes the positions of zeros and there is no zero for closely spaced slits.
The formula is based on a simplified situation with infinitely narrow slits (omnidirectional individual sources)-more like what you get with two co-phased radio frequency dipoles than two slits. If the sources are just greater than λ apart, there will only be a single zero, which will be at nearly 90° off beam. As the spacing gets narrower still, this zero will pass through the 90° direction and disappear. In any case, the beam (the diffraction you are referring to??) pattern of each 'real' single slit will have a zero at 90° or greater. Two dipoles will work fine, though, as a model because they are truly omnidirectional, individually.If the slits are too close together, the phase difference between the waves from the two sources can't be as great as π and so you can't have complete cancellation at 90°. Nevertheless, if there is a reflex angle between the two E vectors, the resulting amplitude will be noticeably lower than where they add and you will get a minimum but the zero is, as you say, at an invalid angle for the formula. I tried a brief search for a suitable diagram of the patterns of two omnidirectional sources on Google but I could find nothing. It's the sort of picture you get in books on antenna theory.
I got to know this stuff from antenna theory, rather than optics and it's actually much more approachable (imo).
If there fringes then there would have to be zeros, wouldn't there? This is just one very broad maximum.terryds said:Will there be any fringes then?
The Young's Double Slit Formula is a mathematical equation used to calculate the interference pattern produced by two slits when a light wave passes through them.
The variables in Young's Double Slit Formula are:
The formula is derived from the principles of wave interference and superposition. When light passes through two slits, it creates a pattern of constructive and destructive interference on the screen. The formula takes into account the path difference between the two slits and the distance from the slits to the screen.
Yes, the formula can be used for any type of wave, as long as the wavelength and distance variables are adjusted accordingly. It has been applied to sound waves, water waves, and even electron waves.
Young's Double Slit Formula is used in various fields such as optics, acoustics, and quantum mechanics. It is used to study interference patterns, measure the wavelength of light, and even determine the size of molecules and atoms. It also plays a crucial role in the development of technologies such as holography and diffraction gratings.