# Diffraction related to Resolving Power

1. Nov 12, 2012

### wizzleman

1. The problem statement, all variables and given/known data

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)?

2. Relevant equations

I tried using

d=(1.22λy)/D

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

3. 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.

2. Nov 12, 2012

### 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.