Resolving Power

Look at these telescope pictures of the same galaxy. Describe how they differ.

On the last picture we can resolve very many more stars than we can on the first picture. Our resolving power is much better.

The resolving power of an optical instrument is the smallest angle at which the light from two point sources can be distinguished as being separate, i.e. resolved.

Imagine you were looking at two points of light close together. ( with one eye ) Walk away from them slowly. At a particular distance you will only be able to see one point of light. The angle between the two sources is the limit of resolution of your eye, i.e. its resolving power. The smaller this angle is, the better your resolving power.

Which of the telescopes below would have a better resolving power?

The second telescope. The main reason why is because it has a much larger aperture. When it comes to telescopes, size matters!

A large aperture means that much more light enters the telescope so the image is brighter.

As light enters through the aperture it diffracts. The image of any particular star is therefore a diffraction pattern. From the equation

the larger the aperture diameter, b, the smaller the angle at which the first minimum occurs.

The image for any star will therefore be less spread out. If the images of two stars are close to each other then they are less likely to "blur" into each other and you are more likely to see them as separate points of light.

There is clearly a link between resolving power and the single slit diffraction pattern.

From Raleigh's criterion 

the limit of resolution of an optical instrument, in radians, is given by ;