Download Experiment 8 Zone Plate Object: 1) To study zone plate 2) To

Experiment 8
Zone Plate
Object:
1) To study zone plate
2) To determine the focal length of zone plates.
Theory:
A zone plate is a screen, made of alternately transparent and opaque zones equal in dimension
to the Fresnel zones and hence covering all even or odd zones. A zone plate can easily be
made in practice by drawing concentric circles on white paper with radii proportional to the
square roots of whole numbers. As in Fig. 1,
1
x  a  a 2  s 2  b  b 2  s' 2
if s  s ' ,
2

x  a 1  1  s 2
a

using 1  x 
1
2
 1
2
 

  b 1  1  s 2 
b
 

1
x  ... and x<<1
2
1
1
s2 s2
x  a[1  (1  ( s 2 ) / a 2 )]  b[1  (1  ( s 2 ) / b 2 )] 

2
2
2a 2b
or
ab
2ab
of the Fresnel zones are such that
  s2 
The radii s m
  m
 sm 
2
2
ab
2ab
Therefore
1 1 m 1
  2 
a b
sm
f
(8-1)
Thus the object and image distances obey the ordinary lens formula. The value of a and b
define two points, called “conjugate” with respect to the given zone plate. The zone plate
concentrates a large fraction of the light coming from one of its conjugate points upon the
second, such as a lens does, Eq. (8-1) shows that the focal length f depends strongly on the
wavelength used. Hence, the zone plate shows chromatic aberration and must be used with
nearly and must be used with nearly monochromatic light.
Arrangement:
Measurement:
1) For source of the six zone plates determine the focal length f by: (I) choosing three
different values of a and finding b (sharp image on the screen) and (II) parallel beam.
Compare your observed values of f with that given on the plate.
2) Explain and demonstrate the fact that the zone plate’s principal planes are coincident with
the plane of the plate itself.
Questions:
1) Why must you use a nearly monochromatic light in using zone plates? Can you
demonstrate it in experiment? Explain.
2) In Arrangement, the position of the screen should be a little more than four times the focal
length of the zone plates, i.e., a + b > 4 f. Why?
3) The zone plate has a positive and negative focal length.
Explain.
Data:
No.
cm. .
23 zone
f/63.07
77 zone
f/45.8
39 zone
f/63.97
19 zone
f/90.46
f(given)
10.5cm
18.0 cm
18.0 cm
18.0 cm
a
b
I
f
f ave
Error
II
f
Error
Reference:
1) Rossi
2) Ditchburn
3) Jenkins
: Optics.
: Light.
: Fundamentals of optics.
P.182
P232
P.385