# Peering into the depths of AskMeApril 20, 2006 9:17 PM   Subscribe

Attention optics geeks: Will a flat water/air port affect a lens' minimum focus distance?

I have a very specialized lens application at work. We need a long telephoto zoom lens (>500mm) which will look through a flat port into a tank of water. I have found a lens [pdf] which meets all of our specs except for one - the minimum focus distance is too long (5m, we need to focus as close as 4m).

I know that the water/air port will increase my effective focal length by about 33%. What I'm wondering is whether the light-bending power of the port might also reduce the minimum focus distance from the manufacturer quoted air-value.

(This isn't my area of expertise)
posted by Popular Ethics to Science & Nature (6 answers total)

It will decrease it slightly. How far it will decrease it is a complex calculation depending on the specific circumstances. Basically, each meter of water will act like the equivalent of a somewhat smaller distance in the air, but how much smaller is among other things a function of how wide the front of the lense is and how far away it is from the flat port. (In other words, it's a function of the angle of incidence.)
posted by Steven C. Den Beste at 10:02 PM on April 20, 2006

The port will decrease the focal distance only slightly compared to the 33% of the air/water transition, as long as the port is relatively thin with respect to the total focal length (assuming that it is flat and your viewing axis is perpendicular to the surface).

I don't know what application you have in mind (surveillance, flow imaging), but would a macro lens work?
posted by swordfishtrombones at 1:03 AM on April 21, 2006

Thanks for the help so far. The application is for inspection, and it has to be a telephoto lens (as opposed to a macro lens) because of the long object distance - 4.5m.

swordfishtrombones: I'm sorry, I don't think I was clear enough. By "will the port reduce...", I don't mean just the glass, I mean the water/glass/air transition. I know what it does to focal length (increase by 33%), but I don't know what it does to min. focus distance.

Steven - that each unit of water is equivalent to a shorter length of air is a useful way of thinking about the problem, thanks. I know you won't be able to give me an absolute value without more numbers, that's OK. I'm just trying to confirm that it won't increase.

That's two votes for decreasing MFD. Any thirders?
posted by Popular Ethics at 4:35 AM on April 21, 2006

OK, thinking about it again this morning, I think my hunch, and the previous answers are wrong. The minimum focusing distance will increase by 33%. Here's my reasoning:

The minimum focussing distance represents the sharpest angle the lens will bend the incident light, and still focus on the image plane. So lets say my aperture is 100mm, and the minimum focus distance is 5m, the incident rays can be no sharper than atan(50/5000), or 0.573 degrees.

Now looking at Snell's law for refraction, sin(angle in water) / sin(angle in air) = 1/1.334. Subing in 0.573 for angle in air, gives me a maximum incident ray in water of 0.429 degrees - smaller!. An incident ray at that angle won't reach the object until 6.6m, or (unsurprisingly I suppose) 33% further from the lens than in air.

I think that reasoning is correct. I would love to be proved otherwise though, because now I have to find a new lens!
posted by Popular Ethics at 7:27 AM on April 21, 2006

indeed. if you look at this drawing you'll see that the fish appears closer than it really is. so, if your fish is 4m from your lens (measured through the water) then it will appear closer and the lens must be able to focus at that "apparent distance".

however, this assumes that the port is right next to the lens. if most of the distance is actually through air then this is not a problem (it struck me that perhaps the 4m distance is "air distance" between the lens and the port/water).
posted by andrew cooke at 9:22 AM on April 21, 2006

I've thought about this some more and realized I got it exactly backward. I agree with the emerging consensus that the real focal length will be longer, not shorter.
posted by Steven C. Den Beste at 11:24 AM on April 21, 2006

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