those of light waves?
1. What is a zone plate? Derive an expression for its focal length ? Compare its
performance to that of a converging leans. How a zone plate is constructed?
(M.D.U Sem IV 2011)
Answers
Answer:
• Zone plate i.e. device used for focussing light exhibiting wave character.
Apart from lenses or curved mirrors zone plates use diffraction instead of reflection.
Analysis by Augustin-Jean Fresnel they are called Fresnel zone plates in honor of him.
Its focusing ability is an extension of Arago spot phenomenon occurred by diffraction from an opaque disc.
Expression of its focal length :
Let S is the source, P is the point of observation and XY is the edge wise section zone plate .
SMn = (a2 + rn2)1/2 = a+ rn2 /2a
rn = √n • (λ) • f.
Hence, focal length of zone plate = rn = √n • (λ) • f
• Comparison of performance of zone plate and Convex Lens (Converging).
• Similarities
Both Zone plate acts a convex lens .
Both are having chromatic aberration while focusing.
The relation between conjugate distances are similar.
• Dissimilarities
a) The zone plate works by diffraction and the lens works by refraction
b) The image produced by a lens is very intense where as the image produced by the zone plate not intense.
c) The zone plate has an array of focal lengths ( N numbers) where as a convex lens has a single focal point.
d) The focal length of a convex lens directly proportional to the wavelength where as the focal length of the zone plate inversely proportional to wavelength.
e) There is no time delay when light is passing through one point to another in the convex lens but there is a time delay as light passes from one period to other in zone plate.
• Construction :
A zone plate is used for focusing light, like a lens. However, light through a lens undergoes refraction but light through a zone plate undergoes diffraction. This is based on the principle of Fresnel Plate and so is known as Fresnel Zone Plate.
A magnifying glass - or a condenser lens - is thick in the middle - a convex lens. It would not be very easy to make a large magnifying glass lens because it would be thick, heavy and hard to mount. A fresnel lens is flat on one side and ridged on the other side.
A magnifying glass - or a condenser lens - is thick in the middle - a convex lens. It would not be very easy to make a large magnifying glass lens because it would be thick, heavy and hard to mount. A fresnel lens is flat on one side and ridged on the other side.
Light rays pass through a traditional convex lens works and are refracted, causing the light to converge into a single point - the focal point, the distance to which is the focal length of the lens.
A Fresnel Lens is a flattened-out version of a convex lens. It was developed in the early 19th century, as a way to reduce the amount of glass material needed to build a convex lens (specifically for large lighthouse lenses, which would have required a huge amount of glass material to create a convex lens of the same diameter). A Fresnel Lens uses the cross-sections of the curvature of a convex lens, but flattens them onto planar surface. That's why the surface of a Fresnel Lens consists of a series of concentric rings - each ring has a slightly different cross-section curvature, corresponding to the curvature of a convex lens of equal diameter.
As a result, you get the same collimated light rays, without all the bulkiness, weight, or glass material needed for a convex lens.
A zone plate consists of a set of radially symmetric rings, known as Fresnel zones, which alternate between opaque and transparent. Light striking the zone plate will diffract around the opaque zones. The zones can be spaced so that the diffracted light constructively interferes at the desired focus, creating an image there.