Determine the angular resolution of a mobile phone camera lens of diameter 2.0 mm atwavelength of 600 nm. [ 2 marks](d) Calculate the maximum distance this camera could resolve the headlights of a car ifthey are separated by a distance of 1.5 m

To solve this problem, we will use the formula for angular resolution which is given by:

θ = 1.22 * (λ/D)

where: θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the lens.

Step 1: Convert the given values to the same units. The diameter D is given as 2.0 mm which is 2.0 x 10^-3 m. The wavelength λ is given as 600 nm which is 600 x 10^-9 m.

Step 2: Substitute the values into the formula:

θ = 1.22 * (600 x 10^-9 m / 2.0 x 10^-3 m)

Solving this gives:

θ = 3.66 x 10^-4 radians

This is the angular resolution of the camera.

For part (d), we need to find the maximum distance at which the camera can resolve the headlights of a car that are 1.5 m apart. We can use the formula:

d = D / tan(θ)

where: d is the distance, D is the separation of the headlights, and θ is the angular resolution.

Substituting the values gives:

d = 1.5 m / tan(3.66 x 10^-4 radians)

Solving this gives:

d ≈ 4100 m

So, the camera can resolve the headlights of a car that are 1.5 m apart at a maximum distance of approximately 4100 m.