Question

Find the minimum aperture diameter of a camera that can resolve detail on the ground the size of a person (2.0 m ) from an SR-71 Blackbird airplane flying at an altitude of 29 km . (Assume light with a wavelength of 450 nm .)

Answer 1

Minimum aperture diameter, B =
`7.96* 10^(-9) = 7.96 mm`

Given:

Altitude of airplane, l = 29 Km = 29000 m

width, d = 2.0 m

wavelength,
`\lambda = 450 nm = 450* 10^(-9)`

Solution:

By Reighley criterion, Angle of resolution
`\theta` is given by:

`\theta_(min) = 1.22(\lambda)/(B)` (1)

Also, separation angle or limiting angle,
`\theta_(min) = (\lambda)/(w)` (2)

From eqn (1) and (2):

`B = 1.22(\lambda* l)/(w)`

`B = 1.22(450* 10^(-9)* 29000)/(2)`

B = 7.96 mm