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From Hobbs Knowledge Base

Summary

When I bought my Nikon D5000 DSLR with a 300mm lens, I took a photo of the moon. I zoomed in as far as I could and to keep the moon in focus I could only make the moon fill about 1/5th of the height of the frame.

I then wondered what focal length I would need to make the moon fill the frame. This started a lunchtime discussion at work, which resulted in the following diagram:

As you can see from the diagram above, if you double the focal length (from Fa to Fb), the subject gets twice as big in the frame (from Sa to Sb).

In the full-size version of the top diagram, for example, the focal length (Fa) is 819 pixels and the distance from the middle of the frame to the middle of the moon (Sa) is 126 pixels.

In the full-size version of the bottom diagram, for example, if we then double the focal length to 1638 pixels (Fb) the distance from the middle of the frame to the middle of the moon doubles to 252 pixels (Sb).

Therefore, if we double the focal length, everything in the frame gets twice the height and twice the width.

So... if the moon shot at 300mm occupies 1/5th of the height of the frame, then in order to make the moon fill the frame, I need to zoom in to 1,500mm.

Example

For example, you can see various photos taken with my camera at different focal lengths below:

	300mm
	150mm
	75mm
	37.5mm
	18.75mm

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