# Where 2 millimeters makes a difference

In an old article, I mentioned that a Canon 18-55mm at high end isnâ€™t that different than the Nikon 17-70mm kit lens in focal length (reach).

My statement was:

After all, you can just shoot the Canon at 55mm @ 1.6x and then crop it down to a 6 megapixel photo and it will look close enough to the Nikon D70 at 70mm at 1.5x.

Iâ€™m surprised nobody has called me out on this statement!

Letâ€™s do the math on the 35mm equivalents: a 55mm 1.6x = 88mm and 70mm 1.5x = 105mm. How different is that? A trick I learned from my Physics graduate advisor: All useful numbers in the world are dimensionless parameters. We have to generate a dimensionless parameter to give meaning to this difference: what we need here is a ratio. How about comparing it to the 35mm format?

55mm/35mm = 1.6. Applying my â€œcropâ€ statement: 1.6*(Sqrt(8M)/Sqrt(6M)) = 1.8. The Nikon example works out to: 105mm/35mm = 3. Hmm thatâ€™s not the same at all!

### An exception proves the rule

What led to my statement was the general rule of thumb: extra focal length makes a difference on the low end than the high. In this case the 70mm on the Nikon still has 50% more reach than the 50mm on the Canon.

Of course weâ€™re talking about 20mm here. When does 2mm make a big difference?

### Going wide

A recent Flickr thread debated between the purchase of the Sigma 10-20mm f/4-5.6 and the Tokina 12-24mm f/4.

Now if you interested in the actual answer to this question, I politely refer you to this venerable Nikonians article which does the best job of comparing them Iâ€™ve seen. How? Well after slogging through Ken Rockwellâ€™s treatise1 I can say that he came to basically an identical conclusion.

The part I want to bring up is when the discussion focused on if you can notice the difference of 2mm. Letâ€™s apply our battery of knowledge.

12mm*1.5/35mm = .51 and 10mm*1.5/35mm = .42.

Yep, that difference (20% I could have just as easily did the ration 12mm/10mm and got the same number) is noticeable. In the thread, I claimed it made â€œa huge difference at wide anglesâ€ but that statement is incorrect. It should have been â€œmakes a noticeable, but not huge difference.â€

### So when does 2mm make a huge difference?

The answer is when you compare the 10.5mm Fisheye Nikkor to my 12-24mm.

The field of view on it is 180 degrees, while the 12-24mm Nikkor has 99 degrees at wide angle. Wow!

Why? Because itâ€™s a fisheye!

As I mentioned in the thread:

The 10.4mm Nikkor has defishing capabilities if you use Nikon Capture, Peter iNovaâ€™s action, LensFix or DxO Optics pro.

I mention this because if you want to go really wide, thatâ€™s probably the way to do it. You have a fisheye and a really wide angle. Youâ€™ll lose resolution near the edges and composition is going to be a pain, but a 10mm fisheye goes much wider than a 10mm rectilinear so the FoV is phenomenal.

Just sayinâ€™â€¦

### How to get even wider

Take a bunch of shots with your 12-24mm and then stitch it together in spherical mode. If you squint a bit, you can pretend you have a fisheye. 🙂

zLunch 2.0
NetService Ventures, Menlo Park, California

Nikon D70, Nikkor 12-24mm f/4G
(15 exposures 1/320sec-1/200sec @ f/8-f/7.1). iso 200, 12mm (18mm)

Of course, you could do the reverse. To know what a de-fished Nikkor might shoot, here is a rectilinear stitch:

Overtop Yosemite Falls
Yosemite Falls Overlook, Yosemite National Park, California

Nikon D70, Nikkor 12-24mm f/4G
5 exposures (1/400 – 1/250sec) @ f/9, iso 200, 12mm (18mm)

I wish I could capture the vertigo I felt taking that shot.

1 The funny thing about reading the article is just when you think Ken has an irredeemable anti-Canon, pro-Nikon bias, you read something like this line: â€œI’d buy the Canon 10-22 mm lens in an instant if I had a Canon digital camera. The Canon 10-22 mm is better than any of these four lenses, including the Nikon.â€ So think about that line next time you Canon people try to paint him with a broad brush.

Iâ€™m curious how Canon was able to do this. Here is and found their optical design in Bobâ€™s review compared to Nikons and theyâ€™re not the same at all! Iâ€™m curious if this is an example of the uniqueness of the EF-S mount (the mount allows lens elements to be further back in the box. The idea is that you donâ€™t need as powerful â€œa telephoto in reverseâ€ optics in order to make the light telecentric (important for digital photography).

Does anyone know?

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