JEE Main & Advanced Physics Wave Optics / तरंग प्रकाशिकी Zone Plate

It is a diffracting device used to experimentally demonstrate the diffraction effect.

(1) It is formed on a glass plate by drawing a number of concentric circles on it whose radii are in the ratio of

\[\sqrt{1}:\sqrt{2}:\sqrt{3}...........\,i.e.\,r\propto \sqrt{n}\]

For some specific distance from this plate the circles coincides with the HPZ's of the Fresnel's theory. (Alternate zones are made opaque).

(2) Positive zone plate : When odd zones are kept transparent to the light and even zones are made opaque, then it is called positive zone plate.

The resultant amplitude due to this zone plate in

\[R={{R}_{1}}+{{R}_{3}}+{{R}_{5}}+..........>>\frac{{{R}_{1}}}{2}\]

Thus, intensity of light tremendously increases.

(3) Negative zone plate : when even zones are kept transparent to light and odd zones are made opaque, then it is called negative zone plate.

The resultant amplitude due to this zone plate is

\[R={{R}_{2}}+{{R}_{4}}+{{R}_{6}}+..........>>\frac{{{R}_{1}}}{2}\]

(4) Zone plate behaves like a convex lens. For a plane wave front the image of source is formed at distance d i.e. d is equal to the principle focal length or first focal length \[{{f}_{1}}=d=\frac{{{r}^{2}}}{\lambda }\]

(5) Multiple focii of zone plate are given by \[{{f}_{p}}=\frac{{{r}^{2}}}{(2p-1)\lambda }\] where p = 1, 2, 3,......... represents the order of foci

(6) If the radius of nth circle on zone plate is \[{{r}_{n}}\] then in terms of \[{{r}_{n}}\].

Principal focal length \[{{f}_{1}}=\frac{r_{n}^{2}}{n\lambda }\]

Other focal length \[{{f}_{p}}=\frac{r_{n}^{2}}{(2p-1)n\lambda }\]

(7) If a is the distance of the source from the zone plate then the distance b of the point where maximum intensity is observes is given by \[\frac{1}{a}+\frac{1}{b}=\frac{n\lambda }{r_{n}^{2}}\]