In class we analyzed the problem of seeing a distant planet. There were two issues:
- Can a telescope resolve a planet?
- Can a telescope detect the light from a planet?
In this problem we want to do the same for your naked eye. We will take some object that emits light and place it far away, and then determine whether you are able to see it. In particular, we will ask the same two questions – not about a telescope, but about your naked eye.
- The first step is to measure the resolving power of your eye. By this we mean that you need to determine the smallest angle qMIN that your eye is capable of resolving. You will need someone else to help you do this: that person writes down some letter on a piece of paper, and then walks far away: you look and see if you can tell what the letter is. Have the person walk towards you until you can just read the letter. Once you have done this, measure the size of the letter and the distance to it, and then use trigonometry to calculate the resolving power qMIN of your eye. Give your answer in minutes of arc. Be careful to describe clearly the method you used: simply writing down the answer will get you no credit whatsoever.
- Now let us suppose that it is a light bulb which we wish to look at. Measure the diameter of a light bulb.
- From what distance are you able to resolve the light bulb? Do the calculation in cgs units, but when you’re through convert your answer to feet to get an intuitive feel for it.
We have now answered question #1 about the light bulb. Now let’s move on to question #2.
- As we saw in class, the human eye is capable of detecting a flux as low as fMIN = 10 – 6 ergs / sec cm2 . Suppose your light bulb has a luminosity of 100 Watts. At what distance can you detect its light? Do the calculation in cgs units, but when you’re through convert your answer to miles to get an intuitive feel for it.
[Note that you can detect light from the light bulb even when it is so far away you cannot resolve it!]