Answer to Question #182703 in Optics for Khushi

Question

What is a zone plate? How does a positive zone plate differ from a negative zone

plate? Show that each Fresnel zone has nearly the same area.

Answer 1

Zone plate: A diffracting device used to experimentally demonstrate the diffraction effect.

Positive zone plate:

• Odd zones are kept transparent to the light
• Even zones are made opaque

Negative zone plate:

• Even zones are kept transparent to light
• Odd zones are made opaque

Proof:

Fresnel subdivided the wavefront into a number of circular zones I, II, III etc. Let PO = b. The area enclosed between O and $O_1$ , $O_1$ and $O_2$ , $O_2$ and $O_3$ etc. are known as half period zones.

Each zone differs from its neighbor by a phase difference of π or a path difference of λ/2. The area enclosed by the first circle of radius $OO_1$ is called the first half period zone.

The area enclosed by the annular strip $O_1O_2$ is known as second half period zone and so on. Thus, the annular area between (n-1)th circle and nth is the nth hall period zone.

Sn ≅ πbλ

Hence, each Fresnel half period zone has nearly the same area.