Question

Determine the farthest away a car can be at night so that your eyes can resolve the two headlights. Assume that the the diameter of your pupil is 0.50 cm, the dominant wavelength emitted by headlights is 500 nm and car headlights are about 1.4 m apart. Express your answer with the appropriate units.

Answer 1

The farthest distance is
`L_(max)=11.48 km`

Step-by-step explanation:

The angular resolution is mathematically represented as

`\theta = (Z)/(L) = (1.22 \lambda)/(d)`

Where Z is the distance between the car head lamp with a value Z = 1.4 m

L is the distance between the eye and the car

`\lambda` is the wavelength with a value 500 nm =
`= 500 *10^(-9)m`

d is the diameter of the eye with a value d = 0.50 cm =
`= (0.50)/(100) = 0.005m`

The maximum distance
`L_(max)` is given as

`L_(max) = ((1.4) *0.005)/(1.22 * (500 *10^(-9)))`

`= 11.48*10^(3)m`

`=11.48 km`

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