# Light (frequency, wavelength etc.)

• tim_3491

## Homework Statement

Imagine that you are in a vehicle at night on a long straight road. There are no streetlights and one vehicle up ahead in the distance.
Estimate how far away the other vehicle would be for its tail-lights to appear as a single
orange/red blob.
• the colour of the light emanating from the tail-lights
• the spatial separation of the tail-lights

## The Attempt at a Solution

red light has lambda = 700nm (700*10^-9m) but now i am not sure what to do. I need to equate/use lambda, lense of an eye and focal length/distance to car.

Have you had the material yet on single-slit diffraction? In this case, you will want to know the angular size of the "central maximum" for diffraction through a circular aperture (the size of the so-called Airy disk). The diameter of the dilated human pupil is about 2 cm. Draw a picture of the triangle formed by the two taillights and the location of your eye. You will want to use the "small-angle approximation" to find the relationship between the apex angle of that triangle, the separation of the lights, and the distance to your eye. The apex angle will equal the angular size of that central maximum when the taillights are at the "limit of resolution", which is the minimum distance at which you will see the two taillights as one light source.