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)1.6 mrad
B)2.2 mrad
C)3.2 mrad
D)4.5 mrad
E)6.3 mrad

Question

Quizplus · Accepted Answer

The maximum aperture diameter is 30 cm which gives a radius of r=15 cm. The diffraction-limited angular resolution can be found from the equation: 
theta = 1.22*wavelength/diameter 
where theta is the angular resolution in radians, wavelength is the light's wavelength, and diameter is the diameter of the aperture. 
Substituting values, we get: 
theta = 1.22*(550 nm)/(30 cm) 
theta = 0.022 rad 
Multiplying by 1000 to convert to milliradians, we get: 
theta = 22 mrad 
However, this is the angular resolution for the entire camera system, not just the lens. To calculate the angular resolution for the lens, we use the formula: 
theta = 1.22*wavelength/f 
where f is the focal length of the lens. 
Substituting values, we get: 
theta = 1.22*(550 nm)/(42 cm) 
theta = 0.016 mrad 
Therefore, the smallest angle subtended by an object on the ground that can be resolved by this camera at maximum aperture is approximately 1.6 mrad. The closest answer choice is B) 2.2 mrad.

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