Question

The normal lens on a 35-mm camera has a focal length of 45.0 mm . Its aperture diameter varies from a maximum of 16 mm (f/2.8) to a minimum of 2.0 mm (f/22).

a.) Determine the resolution limit set by diffraction for f/2.8. Specify as the number of lines per millimeter resolved on the film. Take ? = 560 nm.

b.) Determine the resolution limit set by diffraction forf/22. Specify as the number of lines per millimeter resolved on the film. Take ? = 560 nm.

Answer 1

(a) Resolution is given by
Sin - = 1.22(/D)
Where is wavelength of light and D is dia of lend
= 1.22*(560*10^-9 /35*10^-3)
= 1.952*10^-5 rad
Now for no. of lines in 1 mm
the diameter of the disc (d) = 1.22N
= 1.22*(f) /(f/2.8)
= 1.22*2.8 = 1.22*560*10^-9*2.8
= 1.912*10^-6 m
No. of line = (1*10^-3) /d = 10^-3 /1.912*10^-6
= 523 lines
hence this will be the resolution limit
(b) For f/22
d = 1.22*f / (f/22)
= 1.22*560*10^-9*22
= 15030.4*10^-9 m
No. of lines in 1 mm
= 1*10^-3 / (15030.4*10^-9 )
= 66.53
Hence the resolution limit will be 66.53 for f/22