Question

3. A camera lens has a focal length of 50 mm, and a diameter of 30 mm. If the diaphragm opening (F number) is 5.6. a. Explain the diffraction pattern (FranhouterFa by a circle gap with a diameter D! B. If blue light (450 nm is dropped on the lens, determine the size of the light spot at the focus point! C.) If two adjacent objects are located 10 meters in front of the camera, determine the smallest distance between two objects that can still be seen separately by 1 camera!

Answer 1

lens focal length f = 50mm

aperture F - number f/b = 5.6

aperture dia b = 50 mm/5.6 = 8.93 mm

When light is passed through a circular whole, light is diffracted by the whole. Light from the edges of the circular whole interferes and form alternate bright and dark rigs on the screen at a distance b >> D

radius of the first dark ring R = 1.22 D/b

If the light transmitted by the hole is converged a by a converging lens of focal length f

a bright spot is formed at the focus, of radius

R = 1.22 f/b = 1.22* 450E-9 * 50/8.9 = 3.08E-6 m

B) When light of 450 nm falls on the lens, diameter of the lens itself acts as the aperture and a bright spot is formed at the focus for a distance object. radius of the bright disc

R = 1.22 f/d = 1.22*450E-9 * 50/30 = 9.15E-7 m

C) Object distance 10 m large compared to focus. image formed at focus

radius of the disc = 9.15 E-7 m = 9.15E-4 mm

magnification = v/u = 50E-3/10 = 5.0E-3

if the two objects are seperted by x , then the image distance is

x*5E-3 > 2*9.15E-7 m , so that the two object images are well seperated

x > 3.66 E-4 m = 0.366 mm