# At what distance from the lens will the image be in focus given a subject distance and focal length? [closed]

I've been trying to figure this one out for more than an hour now and I have no idea how to calculate this...

You capture a picture of a tree which is standing 3m away from the camera. The focal length of the camera is 10mm. At what distance from the lens will the image be in focus?

I can't seem to find any equitation or logically come to a solution. Thanks.

``````Possible answers:
1)0.003mm
2)0.233mm
3)5.003mm
4)5.233mm
5)10.033mm
``````
• This sounds like a homework problem. We can help you with that, but it's perplexing because it seems to make some assumptions that do not necessarily match real world photography. If you could explain more about the course you are taking and give more context, that might help. Jan 1 '14 at 15:33
• On your edit: I don't mean adding multiple choice answers. I mean: is this a physics class? Have you done other things with optics? Are you using a certain textbook? What are some other problems in the set? Have you spoken with your teacher? Jan 1 '14 at 16:26
• This question appears to be off-topic because it is about a homework problem in optics where the story problem says "camera" but actually has nothing to do with practical photography and answers based on knowledge of real photographic lenses and cameras will not apply. Jan 1 '14 at 16:33

lens equation

Using the formula (1/S1)+(1/S2)=1/f, in your case S1 = 3m, f = 0.01m, so S2 ~ 0.0103m

• I suspect you are right and the homework assumes that the camera uses a simple "thin lens". For lenses used in actual cameras, it's more complicated and more information is needed. Jan 1 '14 at 15:49
• I've tried using this formula however it does not seem to match one of the possible answers (I've updated the question)
– Dep
Jan 1 '14 at 16:17
• @Dep: Do the math yourself instead of following what Robert has given (because Robert gave the right formula but made a units mistake). Given that this does line up to one of your multiple-choice answers, I think it's safe to say that the problem assumes a thin lens. Jan 1 '14 at 16:31
• Last time I checked 0.0103m is the same distance as 10.033mm. Jun 1 '16 at 7:32

It depends on what distance you aimed your focus. You can do it manually or automatically, but you should know that each lens has it's own limitation and have a minimal focus distance. the maximal focus distance is usually infinity.

This might help: Does changing the focal length change focus?

• I guess you aim your focus at 3m away? That's the whole question that has a particular answer in a number.
– Dep
Jan 1 '14 at 13:47
• If you aim the focus to 3m then the image will be in focus regardless of your focal length (as long as your lens can focus in 3m in the chosen focal length). Jan 1 '14 at 13:59
• I need to give a numeric answer to the question...
– Dep
Jan 1 '14 at 14:05
• There is non, it's totaly depends on the lens. In theory the focal length should not affect the focus. Jan 1 '14 at 14:06
• The answer to life the universe and everything - 42 Jan 1 '14 at 14:18

The focal distance as marked on the lens is the distance from the sensor to the centre of the field of focus. As you use wider lenses and/or narrower apertures, the field of focus will become deeper, meaning that the objects will be in focus at anything from 0.37m to infinity (in the case of a 10mm lens at f/8, set to 3m focal distance).

There are many tools available online where you can work out the field of focus for a given combination of focal length, aperture and subject distance, and no shortage of smartphone apps for a similar purpose (I use PhotoCalc, but others may be able to provide their own recommendations)>

Don't forget that the distance from the LENS to the subject will be the focal distance minus the distance from the sensor to the front element of the lens.