# 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...

*print*Print*list*Cite

### 1 Answer

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:

`c/v =n`

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**

**Sources:**