Answer to Question #171325 in Mechanical Engineering for Thelston

Question

A PIR motion detector made with an infrared faceted fresnel lens has the following properties:

• Focal length of single facet lens = 22.5 mm
• Distance of object from lens = 12.5 m
• Minimum displacement of object which results in detection = 250 mm
• Number of facets = 8

What is the facet pitch in mm?

Answer 1

Focal length of single facet lens = 22.5 mm

Distance of object from lens = 12.5 m

Minimum displacement of object which results in detection = 250 mm

Number of facets = 8

distance from minimum displacement = 12.5m - 250mm = 12.25m

$\dfrac{1}{T}$ = $\dfrac1{12250} - \dfrac1{22.5} = \dfrac{4890}{110250}$

T = 110250/4890 = 22.54mm

facet pitch = 22.54mm/8 = 2.82mm