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Resolving Power

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1) Late 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 1.5 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 (in meters)?

I have worked this problem a couple different ways, don't understand what I am doing wrong but I keep getting 13040.2 meters as the answer.

The first dark fringe in the diffraction pattern of a single slit is located at an angle of theta (sub A) = 25°. With the same light, the first dark fringe formed with another single slit is at an angle of theta (sub B) = 60°. Find the ratio W(sub A)/W(sub B) of the widths of the two slits.

Really dont know where to start on this one.

Help would be much appreciated.

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Sin(Qres) == Qres = D/s = 1.22*lamda/d
where, Qres (theta_res) = angle of resolution = D/s
D = maximum separation of two objects whcih can be resolved. = 1.5 m
s= ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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