Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Take the pupil of an eye to have a diameter of mm. Use light of wavelength nm. Find the smallest angle that this eye can resolve. Find the smallest distance between two points that the eye can tell apart when they are m away. Find also the greatest distance at which two points cm apart can be told apart.
The Rayleigh limit of a circular aperture is . A microscope resolves . A grating has the resolving power .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The angle. .
Step 2. The smallest distance at m. .
Step 3. The greatest distance for points cm apart. .
Answer: rad; cm; m.
Check. A real eye does a little worse than this limit, because of faults in the lens and the spacing of the light-sensitive cells. The limit is for a perfect eye.
Log in to join the discussion.
Loading…