Suppose you are standing on a straight highway and watching a car moving away from you at 20.0 m/s. The air is perfectly clear, and after 11 minutes you see only one taillight. If the diameter of...
The angular separation resolution of a lens is given by
`theta =1.22*lambda/D` , (1)
where `D =7 mm` is the diameter of the lens.
The speed of light is smaller for higher refraction indexes than 1:
which means a shorter wavelength in a medium having a refraction index `n>1`
`lambda =v*T =c/n*T = lambda_0/n`
Combining this with (1) one gets
`theta = 1.22*lambda_0/(n*D)`
The distance from the person to the car is
`L =v*t =20*11*60 = 13200 m`
If `l` is the distance between the taillights one has
`l/L =tan(theta)~~theta =1.22*lambda_0/(nD)`
Thus the for the distance `l` one gets the value
`l =(1.22*lambda_0*L)/(n*D) = (1.22*700*10^-9*13200)/(1.33*0.007) = 1.21 m`
The distance between the taillights is 1.21 m