Question

1. If the incident wave in the Fresnel diffraction is a plane wave (Ro), calculate ro (the distance between the screen and the center of the circular aperture) when there are 6 Fresnel zones in the aperture of 1 mm diameter, using a wavelength of 0.633 um. Will the center of the screen be dark or bright? Briefly explain why 2. If a point light source is 1 m in front of a circuit aperture of 0.6 mm diameter and there are 3 Fresnel zones in the aperture, calculate the imagining point ro assuming the wavelength is 0.633 um

Answer 1

1. Diffraction by circular aperture and Fresnel zone: A circular aperture of radius a, the aperture includes N zones, is give by

$a^{2}=n\lambda r_{0},\ or\ r_{0}=\frac{a^{2}}{n\lambda}=\frac{\left (0.5\times 10^{-3}\ m \right )^{2}}{6\times 0.633\times 10^{-6}\ m}=6.58\ cm$

The definition of the n^th zone can be generalized to be the collection of source points with optical path lengths satisfying

$\frac{(n-1)\lambda }{2}< \Delta r< \frac{n\lambda }{2}$

Here, n is a positive integer from 1 to N, where N is the total number of zones in the zone plate. Source points from odd zones (n=1,3,5,...) will constructively interfere with the 1^st zone, whereas source points from even zones (n=2,4,6,...) will destructively interfere with the 1^st zone. Therefore, it will be dark here.

2. Similarly

$a^{2}=n\lambda r_{0},\ or\ r_{0}=\frac{a^{2}}{n\lambda}=\frac{\left (0.3\times 10^{-3}\ m \right )^{2}}{3\times 0.633\times 10^{-6}\ m}=4.74\ cm$