Diffraction related to Resolving Power

[wizzleman]

Homework Statement

A car passes you on the highway and you notice the taillights of the car are 1.22 m apart. Assume that the pupils of your eyes have a diameter of 7.1 mm and index of refraction of 1.36. Given that the car is 14.1 km away when the taillights appear to merge into a single spot of light because of the effects of diffraction, what wavelength of light does the car emit from its taillights (what would the wavelength be in vacuum)?

Homework Equations

I tried using

d=(1.22λy)/D

where d = 1.22m, D = 7.1mm, y=14.1km

The Attempt at a Solution

I got 5.035x10^-7 as my answer but SmartPhysics keeps on saying that I'm off by a power of ten and I've cycled between negative options but I can't get the answer.

 

[TSny]

Hello.

A couple of things seem odd. If you changed your answer by a power of 10, the wavelength would no longer be in the visible portion of the spectrum.

Your answer is in the visible range, but it corresponds to a bluish-green color (odd for tail lights). See http://www.gamonline.com/catalog/colortheory/visible.php

If you include the effect of the index of refraction, I think you'll get an answer that's much more realistic for tail lights.