How is lens magnification calculated?

Egg Salad · 02-03-2010, 10:27 AM

I know pretty much every 50mm lens has a magnification ratio of 0.15:1 or 1:6.6666...
But I don't get how you get these numbers. I've tried everything logical to me: 50mm:45cm, 5cm:45cm, 45cm:5cm and so on. Nothing comes even close.

So how is this calculated?

imtheguy · 02-03-2010, 01:04 PM

I recently read that the magnification ratio is the actual size of an object to the actual size projected on the camera's sensor. A coin 1cm in diameter shot with a lens having 1:4 magnification would project a 1/4 cm diameter object on the actual sensor or frame of film.

Egg Salad · 02-03-2010, 01:46 PM

Hmmm thanks, but that isn't my question. Determining magnification by simply measuring it is easy. However this is not what I meant.

My question is if you have a lens' focal length and minimum focus distance how do you get its reproduction ratio?

I chose the normal 50mm lens because I know its magnification - but still I can't reconstruct how the values are obtained.

imtheguy · 02-03-2010, 02:04 PM

Ok, I think I see where you are going now. You want the equation that relates focal length and min focus distance to magnification correct? I will do a quick Wikipedia search as its not in my Optics textbook.

imtheguy · 02-03-2010, 02:08 PM

Originally posted by Egg Salad

My question is if you have a lens' focal length and minimum focus distance how do you get its reproduction ratio?

Here is a calculator and below it the theory and equations I think you are looking for.
Lens Magnification and Depth of Field Calculator

By coincidence its on a server maybe not far from you.

p0opstlnksal0t · 02-03-2010, 02:38 PM

i just thought it was the focal length divided by 50mm

Ben_Edict · 02-03-2010, 04:04 PM

I quote from the Link to the magnification calculator, that imtheguy provided:

"However, it still behaves similar to a single thin lens, which collects incoming parallel light rays (from the sun) into one single focal point. Its behaviour can thus be approximated by the well-known lens equation
1 / f = 1 / g + 1 / h (1)

where f is the focal length of the lens, g is the object distance (between object and lens), and h is the image distance (between lens and sensor). "

Obviously this is a bit theoretical, as it uses the simple "thin lens" equation. Modern lenses, especially those with internal focusing (IF) should, I think, not be looked at, as being thin lenses. Not the least, because the focal length changes with focusing distance!

Dimitrov actually illustrates that with Pentax lenses: Focal Length Experiments

The explanations following the above mentioned calculator are, by the way, quite good.

Ben

Egg Salad · 02-03-2010, 05:08 PM

Yes, now this is what I'm talking about.

No, really. That's what I was after.
Yes, I know that calculation only refers to one lens-lenses (isn't there a differentation between one lens and the whole thing - the lens?) but this is also what manufacturers use so it's good enough for me.

Now I could just use the formula but since I'm quite lazy and the internet supports my lazyness I'll just use this calculator.

02-03-2010, 10:27 AM	#1
Egg Salad Veteran Member Join Date: Jul 2009 Location: Berlin, Germany Posts: 344	How is lens magnification calculated? I know pretty much every 50mm lens has a magnification ratio of 0.15:1 or 1:6.6666... But I don't get how you get these numbers. I've tried everything logical to me: 50mm:45cm, 5cm:45cm, 45cm:5cm and so on. Nothing comes even close. So how is this calculated?

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02-03-2010, 01:04 PM	#2
imtheguy Site Supporter Join Date: Mar 2009 Location: Virginia Beach Photos: Gallery \| Albums Posts: 2,950	I recently read that the magnification ratio is the actual size of an object to the actual size projected on the camera's sensor. A coin 1cm in diameter shot with a lens having 1:4 magnification would project a 1/4 cm diameter object on the actual sensor or frame of film.

02-03-2010, 01:46 PM	#3
Egg Salad Veteran Member Join Date: Jul 2009 Location: Berlin, Germany Posts: 344 Original Poster	Hmmm thanks, but that isn't my question. Determining magnification by simply measuring it is easy. However this is not what I meant. My question is if you have a lens' focal length and minimum focus distance how do you get its reproduction ratio? I chose the normal 50mm lens because I know its magnification - but still I can't reconstruct how the values are obtained.

02-03-2010, 02:04 PM	#4
imtheguy Site Supporter Join Date: Mar 2009 Location: Virginia Beach Photos: Gallery \| Albums Posts: 2,950	Ok, I think I see where you are going now. You want the equation that relates focal length and min focus distance to magnification correct? I will do a quick Wikipedia search as its not in my Optics textbook.

02-03-2010, 02:08 PM	#5
imtheguy Site Supporter Join Date: Mar 2009 Location: Virginia Beach Photos: Gallery \| Albums Posts: 2,950	Originally posted by Egg Salad My question is if you have a lens' focal length and minimum focus distance how do you get its reproduction ratio? Here is a calculator and below it the theory and equations I think you are looking for. Lens Magnification and Depth of Field Calculator By coincidence its on a server maybe not far from you.

02-03-2010, 02:38 PM	#6
p0opstlnksal0t Senior Member Join Date: Oct 2009 Location: houston Posts: 165	i just thought it was the focal length divided by 50mm

02-03-2010, 04:04 PM	#7
Ben_Edict Veteran Member Join Date: Jul 2007 Location: SouthWest "Regio" Photos: Albums Posts: 3,309	I quote from the Link to the magnification calculator, that imtheguy provided: "However, it still behaves similar to a single thin lens, which collects incoming parallel light rays (from the sun) into one single focal point. Its behaviour can thus be approximated by the well-known lens equation 1 / f = 1 / g + 1 / h (1) where f is the focal length of the lens, g is the object distance (between object and lens), and h is the image distance (between lens and sensor). " Obviously this is a bit theoretical, as it uses the simple "thin lens" equation. Modern lenses, especially those with internal focusing (IF) should, I think, not be looked at, as being thin lenses. Not the least, because the focal length changes with focusing distance! Dimitrov actually illustrates that with Pentax lenses: Focal Length Experiments The explanations following the above mentioned calculator are, by the way, quite good. Ben

02-03-2010, 05:08 PM	#8
Egg Salad Veteran Member Join Date: Jul 2009 Location: Berlin, Germany Posts: 344 Original Poster	Yes, now this is what I'm talking about. No, really. That's what I was after. Yes, I know that calculation only refers to one lens-lenses (isn't there a differentation between one lens and the whole thing - the lens?) but this is also what manufacturers use so it's good enough for me. Now I could just use the formula but since I'm quite lazy and the internet supports my lazyness I'll just use this calculator.