Answer
a) The f-number $2.8$ gives the largest diameter.
b)
$ D_1\approx 20mm $
$ D_2\approx14mm $
$ D_3=6.9mm $
$ D_4=5.0mm $
$ D_5=3.43mm $
Work Step by Step
(a) We know that the diameter of the aperture is inversely proportional to the f-number. The f-number with the smallest value will give us the largest diameter and thus the f-number $2.8$ gives the largest diameter.
(b) We can find the required diameter of the aperture as follows:
$ D_1=\frac{f}{f_{number}}$
We plug in the known values to obtain:
$ D_1=\frac{55mm}{2.8}$
$ D_1=19.6mm $
$ D_1\approx 20mm $
$ D_2=\frac{55mm}{4}$
$ D_2=13.75$
$ D_2\approx14mm $
$ D_3=\frac{55mm}{8}$
$ D_3=6.9mm $
$ D_4=\frac{55mm}{11}$
$ D_4=5.0mm $
$ D_5=\frac{55mm}{16}$
$ D_5=3.43mm $
