i wonder how we can describe the degree of diffraction of waves in a single slit in a mathematical formula , with the variables , wavelength and slit width ....my attempt to it is to use the equation for double-slit interference(or plane transmission grating) , namely 'd sin theta=n lambda' ...it is clearly shown that lambda is directly proportional to the value of sin theta while the slit separation is inversely proportional to it....as the value of sin theta is also related to the degree of diffraction of the two diffracted waves.....the equation can also be applied to describe the degree of diffraction of waves in a single slit.......does anyone have other suggestions? another question , how can the diffracted waves form alternating dark and bright fringes on a screen ? it makes me hard to distinguish 'interference' and 'diffraction'
Wikipedia already has a discussion and mathematical description of single slit diffraction. http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction Interference arises because the opening of the slit acts as sources of the wave diffraction. If the slit is wide enough (on the order of a wavelength), then these sources over the opening have a large phase shift between them which gives rise to interference in the diffracted wave. At small slit separations, there is little phase (and spatial) difference between them and the slit acts as a coherent source.
You are correct to give the equation dSinθ = nλ as the one to use to find the positions of MAXIMA when you have 2 sources (slits) producing interference. When there is only one slit the distance 'd' indicates the width of the slit, usually the letter 'a' is used. The rest is in the mathematics !!!!! For a slit of width 'a' MIMINA occur when aSinθ = nλ. i.e the angle at which MINIMA occur is given by Sinθ= nλ/a. As an example, when a = λ the first (n=1) minimum occurs when Sinθ = 1, ie at 90 degrees So a slit of width mone wavelength allows waves to pass through at all angles 0 to 90..... it is a point source. When a = 2λ the first minimum is at 30 degrees and the second minimum is at 90 degrees.... interference is ocurring to produce a more complex diffraction pattern.