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

Answer:

Minimum aperture diameter, B = $7.96\times 10^{-9} = 7.96 mm$

Given:

Altitude of airplane, l = 29 Km = 29000 m

width, d = 2.0 m

wavelength, $\lambda = 450 nm = 450\times 10^{-9}$

Solution:

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

$\theta_{min} = 1.22\frac{\lambda}{B}$                            (1)

Also, separation angle or limiting angle, $\theta_{min} = \frac{\lambda}{w}$        (2)

From eqn (1) and (2):

$B = 1.22\frac{\lambda\times l}{w}$

$B = 1.22\frac{450\times 10^{-9}\times 29000}{2}$

B = 7.96 mm