Telescopes

Telescopes are devices that allow observers to gather and focus light to make an image. They utilize lenses which have a diameter $$d$$ and a focal length $$r$$

Varying Diameter
Varying the diameter of the apperature varies the amount of light that can come in through the apperature. The amount of light collected varies directly with the area of the apperature.

Varying Focal Length
Focal length directly controls the size of the image that is created. This is because the height of an image coming in at angle $$\theta$$ is:

$$y = f tan\theta$$