Question

what is the radius of half period zone in a zone plate behaving like a convex lens of focal length 60cm for light of wavelength 6000anstrom

Answer 1

One common use of a zone plate is to bring light from a distant source to focus. In this scenario, the incident wave can be approximated as a plane wave.

Positioning of zone boundaries

In this section, zone radii will be derived for a zone plate optic with focal length ff.

To begin, consider a source point in the plane of the zone plate located a distance rr from the center of the zone plate.



The distance ll between the source point and the focus is called the optical path length, and is given by:

l=r2+f2−−−−−−√(1)(1)l=r2+f2

The optical pathlength from a source point at the center of the zone plate (r=0r=0) is simply equal to the focal length.

l0=f(2)(2)l0=f



The goal is to locate source points that constructively interfere at the focus. This is accomplished by requiring that optical path lengths ll differ by no more than λ/2λ/2 from the optical pathlength of the on-axis source l0l0.

l−l0<λ2(3)(3)l−l0<λ2

Source points satisfying this criterion define the 1st zone, which is shaded in red below:



Answer 2

500 anstrom is the radious of wavelength of focal length