Question

You've got binoculars with 28-mm-diameter lenses. You're observing two bees on a flower 840 m distant. What's the minimum separation between the bees for you to be able to resolve them as two distinct insects? Assume visible light with 550-nm wavelength.

Answer 1

Using the Rayleigh criterion and the given values for the lens diameter and the wavelength of visible light, we can calculate the minimum separation between the bees that the binoculars can resolve.

The minimum separation between the bees for them to be resolved as two distinct insects is 16.44 m.

Step-by-step explanation:

The minimum separation between two objects required to be able to resolve them as two distinct objects is determined by the diffraction limit of the optical system. The formula for the angular resolution (Δθ) in radians is given by λ / D, where λ is the wavelength of light and D is the diameter of the lens or aperture.

In this case, we have a binoculars with 28-mm-diameter lenses and we want to observe two bees 840 m away. The minimum separation between the bees for them to be resolved as two distinct insects can be calculated as follows:

Angular resolution = λ / D

= 550 nm / 28 mm

= 0.0196 radians

We can convert this angular resolution to a linear separation by multiplying it by the distance to the object. Therefore, the minimum separation between the bees is 0.0196 radians * 840 m = 16.44 m.