Question

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

The minimum separation between the bees for them to be resolved as two distinct insects is approximately 4.2 mm.

Step-by-step explanation:

The minimum separation between the bees for you to be able to resolve them as two distinct insects can be calculated using the formula for minimum resolvable angle in the context of diffraction:

θ = 1.22 * (λ / d)

Where θ is the angle, λ is the wavelength, and d is the separation distance between the bees. Converting the separation distance of 6.5 cm to meters and the wavelength of 510 nm to meters, we have:

θ = 1.22 * (510e-9 m / 0.065 m) = 9.506e-6 radians

To find the corresponding distance, we can use the formula:

Distance = tan(θ) * pupil diameter

Substituting values:

Distance = tan(9.506e-6 radians) * 5.0 mm = 4.2 mm

Therefore, the minimum separation between the bees for them to be resolved as two distinct insects is approximately 4.2 mm.