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 pup

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.

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Gerda 6 months 2021-07-26T22:14:58+00:00 1 Answers 6 views 0

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    2021-07-26T22:16:24+00:00

    Answer:

    The farthest distance is L_{max}=11.48 km

    Explanation:

    The angular resolution is mathematically represented as

                  \theta = \frac{Z}{L} = \frac{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 = = \frac{0.50}{100} = 0.005m

       The maximum distance L_{max} is given as

                  L_{max} = \frac{(1.4) *0.005}{1.22 * (500 *10^{-9})}

                           = 11.48*10^{3}m

                            =11.48 km

                 

    rrrrrrr

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