Question

you've got binoculars with 28-mm -diameter lenses. you're observing two bees on a flower 580 m distant. part a what's the minimum separation between the bees for you to be able to resolve them as two distinct insects? assume visible light with 510- nm wavelength. express your answer with the appropriate units.

Answer 1

To resolve two distinct insects using binoculars, the minimum separation between them needs to be greater than the resolving limit determined by the Rayleigh criterion. For the given lens diameter of 28 mm and wavelength of 510 nm, the minimum separation is calculated to be 12785 arcseconds when observing bees 580 m distant.

Step-by-step explanation:

To resolve two distinct insects, the minimum separation between them needs to be greater than the resolving limit determined by the Rayleigh criterion. According to the Rayleigh criterion, the resolving limit is given by the formula:

θ = 1.22 * (λ / D)

Where:

• θ is the resolving angle
• λ is the wavelength of light
• D is the diameter of the lens

In this case, the lens diameter is 28 mm and the wavelength of light is 510 nm. Plugging in these values, we can calculate the minimum resolving angle:

θ = 1.22 * (510 nm / 28 mm) = 22.07 arcseconds

To find the minimum separation between the bees, we can use the formula:

separation = distance * θ

Given that the bees are 580 m distant, we can calculate the minimum separation:

separation = 580 m * 22.07 arcseconds = 12785 arcseconds

Therefore, the minimum separation between the bees for you to be able to resolve them as two distinct insects is 12785 arcseconds.