Surely it must be universally true of photographers that no matter what size of telephoto lens you have, you always want something even bigger (Nikon include a 1.4x teleconverter as standard with their mammoth 800mm lens). But how much extra reach do you get for what will undoubtedly be a huge investment? Well below, for interest, I show every principal focal length from 50mm - 1,000mm so you can see where that gets you.

I hope that was interesting. What you might have noticed however is that while 800mm obviously takes you in closer than 700mm, there seems to be a law of diminishing returns compared with say the gain you get zooming from 100mm to 200mm. This is because the area of an image is proportional to the square of the focal length of the lens. Let me explain that.

Assume you take a picture of a house that has dimensions 6 metres by 4 metres. Let's say you fill the frame with a 100mm lens. The overall image captures an area of 24 square metres (6 x 4 = 24). Now, if you double the focal length to 200mm, the part of the house you captures is halved, ie, 3 metres by 2 metres, but overall, this means that you capture just 6 square metres (3 x 2 = 6).

In other words, when you double the focal length, the larger lens crops in to produce that portion of the image four times as large (area wise) as the smaller focal length (24/6 = 4), or another way to arrive at the same result, square the focal length of the two lenses, ie 200mm squared (40,000) divided by 100mm squared (10,000) gives a factor of 4. You actually don't need those zeros, 2 squared divided by 1 squared = 4.

Now it is clear: the gain between a 500mm lens and a 600mm lens is 6 squared divided by 5 squared = 36/25 = 1.44, nowhere near as much as the factor of 4 when you double the focal length such as you do in going from 50mm to 100mm, or from 100mm to 200mm.

Gain factors for each jump in lens size are shown below:

50mm to 100mm: 4.0

100mm to 200mm: 4.0

200mm to 300mm: 2.25

300mm to 400mm: 1.78

400mm to 500mm: 1.56

500mm to 600mm: 1.44

600mm to 700mm: 1.36

700mm to 800mm: 1.31

800mm to 1000mm: 1.56

Assume you take a picture of a house that has dimensions 6 metres by 4 metres. Let's say you fill the frame with a 100mm lens. The overall image captures an area of 24 square metres (6 x 4 = 24). Now, if you double the focal length to 200mm, the part of the house you captures is halved, ie, 3 metres by 2 metres, but overall, this means that you capture just 6 square metres (3 x 2 = 6).

In other words, when you double the focal length, the larger lens crops in to produce that portion of the image four times as large (area wise) as the smaller focal length (24/6 = 4), or another way to arrive at the same result, square the focal length of the two lenses, ie 200mm squared (40,000) divided by 100mm squared (10,000) gives a factor of 4. You actually don't need those zeros, 2 squared divided by 1 squared = 4.

Now it is clear: the gain between a 500mm lens and a 600mm lens is 6 squared divided by 5 squared = 36/25 = 1.44, nowhere near as much as the factor of 4 when you double the focal length such as you do in going from 50mm to 100mm, or from 100mm to 200mm.

Gain factors for each jump in lens size are shown below:

50mm to 100mm: 4.0

100mm to 200mm: 4.0

200mm to 300mm: 2.25

300mm to 400mm: 1.78

400mm to 500mm: 1.56

500mm to 600mm: 1.44

600mm to 700mm: 1.36

700mm to 800mm: 1.31

800mm to 1000mm: 1.56