Final answer:
This high school Physics problem involves calculating the maximum distance at which car headlights, 1.3 m apart, can be resolved by the human eye, using the Rayleigh criterion and assuming an average wavelength of visible light. The pupil diameter of the eye is taken to be 0.40 cm.
Step-by-step explanation:
The question refers to the ability of the human eye to resolve two point sources of light, such as the headlights of a car, at a certain distance. This is a Physics problem that can be solved using the Rayleigh criterion, which states that two sources are just resolvable when the central maximum of the diffraction pattern of one source lies on the first minimum of the diffraction pattern of the other source.
The equation for the Rayleigh criterion is given as:
θ = 1.22 * λ / d
where θ is the angular resolution, λ is the wavelength of light, and d is the diameter of the aperture (in this case, the pupil of the eye).
By rearranging the formula to solve for the maximum distance (D) at which two headlights can be resolved, we find that:
D = 1.22 * λ * L / d
where L is the distance between the two headlights and λ is assumed to be an average wavelength for visible light (approximately 550 nm).
Using the given values of L = 1.3 m and d = 0.40 cm, and assuming an average wavelength λ of 550 nm (5.50 x 10^-7 m), we can calculate the maximum distance at which car headlights can be resolved.