Repeal parts (a) and (b) of problem 1 when the source is a point source 10 cm from the ape...

Repeal parts (a) and (b) of problem 1 when the source is a point source 10 cm from the aperture. Take into account the results of problem 2.

Problem 1–2

1. Plane waves of monochromatic (600-nm) light are incident on an aperture. A detector is situated on axis at a distance of 20 cm from the aperture plane.

a. What is the value of R1, the radius of the first Fresnel half-period zone, relative to the detector?

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b. If the aperture is a circle of radius 1 cm, centered on axis, how many half-period zones does it contain?

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c. If the aperture is a zone plate with every other zone blocked out and with the radius of the first zone equal to R1 (found in (a)), determine the first three focal lengths of the zone plate.

2. The zone plate radii given by Eq. (13-20) were derived for the case of plane waves incident on the aperture. If instead the incident waves are spherical, from an axial point source at distance p from the aperture, show that the necessary modification yields

where q is the distance from aperture to the axial point of detection and L is defined by 1/L = 1/p + 1/q.

Figure 1.