We imagine that a point source of light at illuminates an aperture in an opaque barrier located at as shown below.
The irradiance of the light appearing at point on the viewing screen located at is then given by
where is a constant, is the distance from (the source) to (the screen point), and is a function we call the ‘transparency function’. If the line from the source at to the screen point passes through the aperture, then ; otherwise, . In the case where the aperture is a rectangle of width in the -direction and height in the -direction, show that the value of the transparency function is given byAlt Figure
Compute the irradiance on an array of uniformly spaced screen points on the viewing screen for an aperture with cm and cm in the following cases:
[cm] | [cm] | [cm] | [cm] |
---|---|---|---|
0.0 | 0.0 | -20.0 | 40.0 |
5.0 | 0.0 | -20.0 | 40.0 |
0.0 | 5.0 | -20.0 | 40.0 |
0.0 | 0.0 | -10.0 | 40.0 |
0.0 | 0.0 | -40.0 | 40.0 |
0.0 | 0.0 | -20.0 | 60.0 |
0.0 | 0.0 | -20.0 | 20.0 |
Does the computed light pattern change as you expect when you change the source and screen locations? Are the edges of the light pattern sharp or fuzzy? (How do you define “sharp” and “fuzzy”?) Why?