Find the minimum aperture diameter of a camera that can resolve detail on the ground the size of a person (1.5 m ) from an SR-71 Blackbird airplane flying at an altitude of 26 km . (Assume light with a wavelength of 470 nm .)
I got 570 mm which is wrong
To find the minimum aperture diameter of a camera that can resolve detail on the ground the size of a person from a given altitude, we can use the concept of angular resolution.
The angular resolution of an optical system is determined by the wavelength of light and the diameter of the aperture. The smaller the wavelength and the larger the aperture diameter, the better the resolution.
In this case, the camera is capturing detail from a distance of 26 km, and we want to be able to resolve an object the size of a person, which is approximately 1.5 m.
To calculate the minimum aperture diameter, we need to determine the angular resolution required to distinguish the size of the person at that distance.
The formula for angular resolution is given by:
θ = 1.22 * (λ / D)
where:
θ is the angular resolution (in radians),
λ is the wavelength of light (in meters),
D is the aperture diameter (in meters).
Given:
λ = 470 nm = 470 * 10^-9 m
Distance to the ground = 26 km = 26,000 m
Size of the person = 1.5 m
First, we need to find the angle subtended by the person on the camera:
θ = size of the person / distance to the ground
θ = 1.5 m / 26,000 m
Now, we can rearrange the formula for angular resolution and solve for D:
D = λ / (1.22 * θ)
D = 470 * 10^-9 m / (1.22 * θ)
Substituting the value of θ we calculated earlier, we can determine the minimum aperture diameter.
Please note that the value obtained will be in meters. Convert it to millimeters if needed.
Using this approach, you should be able to calculate the correct minimum aperture diameter.