# Homework Help: Resolving Power and diffraction

1. Apr 11, 2007

### Dart82

1. The problem statement, all variables and given/known dataLate one night on a highway, a car speeds by you and fades into the distance. Under these conditions the pupils of your eyes (average refractive index = 1.36) have diameters of about 7.0 mm. The taillights of this car are separated by a distance of 1.3 m and emit red light (wavelength = 660 nm in vacuum). How far away from you is this car when its taillights appear to merge into a single spot of light because of the effects of diffraction?
[URL=http://img58.imageshack.us/my.php?image=resolvingpoweruz3.jpg][PLAIN]http://img58.imageshack.us/img58/1871/resolvingpoweruz3.th.jpg[/URL][/PLAIN]

2. Relevant equations
s=r(theta)
Rayleigh criterion for resolution: theta min = 1.22 (lambda/D)

3. The attempt at a solution

lambda eye = lambda vacuum/ n eye
(660x10^-9m) / 1.32 = 5x10^-7m

1.22(lambda eye/D)=s/r
1.22(5x10^-7m)/0.007m = 1.3m/r
r = 15385 meters
What am i doing wrong here??

Last edited: Apr 11, 2007
2. Apr 11, 2007