Question

Suppose you are looking down at a highway from a jetliner flying at an altitude of 6.0 km. How far apart must two cars be if you are able to distinguish them? Assume that λ=550nm and that the diameter of your pupils is 4.0 mm.

Answer 1

To distinguish two cars from a certain altitude, we need to consider the phenomenon of diffraction and calculate the angle between two just-resolvable points of light.

Step-by-step explanation:

In order to determine how far apart two cars must be in order for you to distinguish them, we need to consider the phenomenon of diffraction.

According to the theory of diffraction, the angle between two just-resolvable points of light can be calculated using the formula:

θ = 1.22(λ/d)

Where θ is the angle, λ is the wavelength of light, and d is the diameter of the pupil.

Given that the wavelength of light is 550 nm and the diameter of your pupil is 4.0 mm, we can calculate the angle as:

θ = 1.22(550 nm / 4.0 mm)

By using a tangent function, we can then calculate the distance between the two cars:

Distance = Altitude * tan(θ)

Therefore, the two cars must be at least this distance apart for them to be distinguishable.