A camera used for aerial mapping has a lens with a 30-cm diameter maximum aperture and a 42-cm focal length. Light of 550 nm wavelength is used to form the image. Assuming that the
Resolution of the camera is limited only by diffraction, what is the smallest angle (in milliradians)
Subtended by an object on the ground that can be resolved by this camera at maximum aperture?
A) 6.3 mrad
B) 1.6 mrad
C) 4.5 mrad
D) 2.2 mrad
E) 3.2 mrad

Question

Quizplus · Accepted Answer

The resolution limit due to diffraction for a circular aperture is given by the formula $\theta = 1.22 \frac{\lambda}{D}$, where $\theta$ is the angle in radians, $\lambda$ is the wavelength of light, and $D$ is the diameter of the aperture. Substituting $\lambda = 550 \times 10^{-9}$ meters (or 550 nm) and $D = 0.3$ meters (30 cm) into the formula gives $\theta = 1.22 \times \frac{550 \times 10^{-9}}{0.3} = 2.233 \times 10^{-3}$ radians, or 2.233 milliradians, which rounds to approximately 2.2 mrad.

A Camera Used for Aerial Mapping Has a Lens with a 30-Cm