Physics, 25.06.2020 02:01 rsnyder

You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.681 m apart. At what distance, in kilometers, are you marginally able to discern that there are two headlights rather than a single light source

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Answer from: drinkinwater

Complete Question

You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.681 m apart. At what distance, in kilometres, are you marginally able to discern that there are two headlights rather than a single light source?Take the wavelength of the light to be 549 nm and your pupil diameter as 4.63 mm.

The distance is $z = 4707.6 \ m$

Explanation:

From the question we are told that

The is distance between the headlight is $d = 0.681 \ m$

The wavelength is $\lambda = 549 \ nm = 549 *10^{-9} \ m$

The pupil diameter is $D = 4.63 \ mm = 0.00463 \ m$

Generally, we can mathematically evaluate the resolution of the eye as

$\theta = \frac{1.22 * \lambda }{D}$

substituting values

$\theta = \frac{1.22 * 549 *10^{-9} }{0.00463}$

$\theta = (1.45 *10^{-4} )^o$

Now according to SOHCAHTOA rule

$sin \theta = \frac{ d}{z}$

Where z is the distance at which the eye can discern the two head light

given that the angle is very small $sin \theta = \theta$

=> $\theta = \frac{ d}{z}$

substituting values

$1.45*10^{-4} = \frac{ 0.681}{z}$

=> $z = \frac{0.681}{1.45 *10^{-4}}$

=> $z = 4707.6 \ m$

Answer from: Quest

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

Answer from: Quest

1.state2.trash3.the earth

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You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equi...