a camera is used to take picture of an object this object is

a camera is used to take picture of an object .this object is 5mmaway from camera.the height of the object is 1.7m. the cmos camera arryhas a single pixel size of 2um located in the focal plane of 4mm away .please calculate how many pixels will be covered by the image. if i use a F-number F5.6 when i take the picture what is the etendue of this camera

Solution

The camera uses a convex lens.

Focal length of the camera (f) .

Here it is said that the image is located in a focal plane of 4mm away

Hence we take, image distance (v) = 4mm = 0.004 m

Object distance (u) = 5 mm =0.005m

Hence the image distance(v) can be calculated using the lens formula:

(1/v) - (1/u) =(1/f)

or, f=0.02m = 20mm

Magnification m = (image height h/object height H) = -v/u= 4/5 = 0.8

Hence image height = 1.7 * 0.8 m =1.36 m = 1360mm

Single pixel size = 2um = 0.002 mm

Hence number of pixels required = 1360/0.002= 680000

Etendue is the product of the pixel solid angle field of view with the lens aperture area

Aperture is the lens opening area and it is measured in mm.

So 20mmf/5.6 will have aperture 20/5.6 mm = 3.57143 mm

This will give the requied etendue