Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Detail Summery about Fresnel’s class Diffraction, Fresnel’s half - period zones , Diffraction by an opaque Disc – The Poisson Spot, The zone –plate, mutually interfere, Huygens – Fresnels principle.
Typology: Study notes
1 / 13
This page cannot be seen from the preview
Don't miss anything!
To explain Fresnel’s class difrection we use Huygens – Fresnels principle according to which: Each point on a wavefront is a source of secondary disturbance and the secondary wavelets emanating from different points mutually interfere. We know that the incidence beam will undergo diffraction divergence and the angular spreading will be given by Δθ ~ λ/2a
If a >> λ, the intensity at a point R will be negligible; on the other hand , if a ~ λ there will be almost uniform spreading out of the beam resulting in an uniform illumination of the screen.
We make some construction as shown in the fig.
Let us consider a plane wavefront WW’. The annular area between nth and (n-1)th cricle is known as n th half period zone. The area of the n th half – period zone is given by A n = πr 2 n
n+ u n
The resultant amplitude at P u(P) = u 1 /2, for large n Thus, the resultant amplitude produced by the entire wavefront is only one half of the amplitude produced by the first half-period zone.
By using the Fresnels half period zones theory we can study the diffraction of a plane wave by a circular aperture. In fig 1. if we increase the radius of circular aperture, when a = √λd, then u (P) = u 1 = 2 ( amplitude for the unobstructed wavefront). and when a = √2λd, then u(P) = (u 1
If instead of circular aperture, we have a circular disc (see Fig.3) and if the disc obstructs the first p half period zones then the resultant field at the point P would be u (P) = u p+
= u p+
Thus, we should always obtain a bright spot on the axis behind a circular disc. This is called the ‘Poisson spot’.
A zone plate is a beautiful application of the concept of Fresnels half – period zones, which consists of a large number of concentric circles (see Fig4) and have following properties :- (i). The areas of the half period zones are equal. (ii). The redii of half period zones are proportional to the square root of th natural numbers. i.e r n = √nk (iii). If the light is obstructed from alternate zones, the intensity of the image is sufficiently increased. As we know u(P) = u 1
If the light is obstructed from even half period zones then u(P) = u 1
There are two types of Zone Plate :- Positive and Negative Zone Plate. If the odd (even) numbers are covered with black ink, and an accurate photograph of this is taken on a glass plate of uniform thickness. In the negative of the photograph of the glass plate, the odd (even) zones which are painted black appear transparent and the even (odd) zones appear black. The resulting glass negative is known as positive (negative) zone plate
