# Fresnel zone plate diffraction

## Homework Statement

A zone plate is to be set up on an optical bench, where it will be used as an enlarging lens. Its innermost zone is to be 0.2250 mm in diameter and monochromatic blue-green light of wavelength 480 nm from a cadmium arc is to be used. If the magnitude of the enlargements is to be eightfold in diameter, find:

(a) the focal length of the zone plate and
(b) the object distance and
(c) the image distance.

## Homework Equations

where n is an integer, r is the radius, and r_N and delta r_N are the outermost zone radius and its width.

## The Attempt at a Solution

this is my diagram which shows my current understanding of whats going on. i dont think it was taught very well in lectures and either im not searching for the right thing on the net, or theres not information on this problem, or its so basic no one has bothered to put up any information on it. at the moment i dont really know where to go from here. we're given r_1 or r_0 (not sure if its 1 or 0), the wavelength and the enlargement magnitude. it looks like im gonna have to use some tricky geometry or something but im honestly not sure what to do.

Last edited:

Ibix
You should be able to tell from the first equation whether the quoted radius is $r_0$ or $r_1$.

Given that, it looks like you've got (a) from the first equation.

For monochromatic light you can basically treat a Fresnel lens as a "regular" thin lens (they have brutal chromatic aberration, though, and their off-axis performance isn't great, if memory serves). So parts (b) and (c) come from the usual lens formulae relating focal length and magnification to object and image distances.

ahh i see, first equation gives 10.5cm for f. that was simple, why didnt i see that before?? now i was thinking we just use the thin lens equation in the first place since all it was doing is the same thing a thin lens would do, but i wasnt sure because i dont fully understand whats going on in the zone plate. alright so thats answered everything basically, thanks! one last thing, is my diagram correct?

Ibix