## Magnification Calculations

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Kevin Childress
Posts: 24
Joined: Fri Aug 14, 2015 2:19 pm
Location: Lowell, North Carolina
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### Magnification Calculations

Greetings from a forum newbie! I'm hoping to find a macro-mathematician to help me validate the total lens magnification involved with a particular lens arrangement. I hate to ask anyone to crunch numbers for me but admittedly I'm having trouble with some of this. My only understanding of the math is to break it down to granular pieces. Please set me straight if I misunderstand or mis-speak any of this.

The scenario is this: 27.5mm extension tube (plus) Nikon AF-S DX 1:1 Macro 85mm f/3.5 (plus) a reversed Nikon 50mm AF-S f/1.8.

I consistently find reference to the same calculations used to determine magnification power for these components. Taking the reversed 50mm lens standalone for example, everything I find says the reversed 50 should act as a +20 diopter (the formula being: 1000mm / focal length of lens = +20 diopter). Then, translating a +20 diopter is supposed to be 6x magnification (the formula being: +20 diopter / 4 + 1 = 6x power). So my first question is do you agree the reversed 50mm lens alone provides 6x magnification?

And then we have the 85mm 1:1 macro lens with 27.5mm of extension tube. According to an extension calculator found at Cambridge In Color, this combination should provide 1.32x magnification (the formula being: 27.5mm extension tube / 85mm focal length + 1.0 lens reproduction ratio = 1.32x). Question 2: Does this sound accurate and can this be refined?

What I really don't understand is how we combine the magnification powers of the separate components. Is it a simple matter of multiplying one by the other (6x * 1.32x = 7.92x)??

The thing is I don't believe for a second that I'm getting anywhere close to 7x with the combination described above. I tend to believe what I can see, touch, and feel. And since we can measure pixels very precisely in Photoshop, what I'm seeing is consistently between 3.46x and 3.49x over a known 1:1 baseline. I could round that down to 3.4x and be quite happy.