[Harris, David]

Harris, David  asked the Naked Scientists:
   
Being of a certain age, I find myself needing reading glasses to see anything closer than arm's length very clearly. 

However, if I peer through a small hole the size of a pencil lead in a piece of paper for example, I am able to see things very clearly at a remarkably close range. 

I have, in fact, used this on occasion when I have forgotten my glasses.  How does this work?
 
Sincerely,

Ben Harris
North Carolina, USA

What do you think?

[JP]

Hi Ben,

There are a few different ways of explaining this.  The way I prefer is to think of rays.  You can think of rays coming out in all directions from every point of an object that you're looking at.  A bunch of these rays will strike different points on your eye.  If you have a perfect lens in your eye, it focuses all these different rays onto one point on your retina.  This means, for a perfect eye, each point on the is imaged to a perfect point on your eye.  Of course, eyes aren't perfect and they get worse as we age, so rays striking one part of your eye's lens might get sent to a slightly different place than rays striking another part of your eye's lens.  The result is a blurring of the object, since points on the object get smeared out on your retina.

If you put a pinhole in front of your eye, you're basically allowing only a small number of rays through from each point on the object.  These all strike the lens of your eye in roughly the same place, and since the lens in your eye is fairly good over small areas, they all form a much less blurry point on your retina, forming a clearer image.  In theory, the smaller you make the pinhole, the better image you form, but the trade-off is that you let less light through, so whatever you're looking at becomes dimmer.

[Geezer]

Good explanation JP.

Another way of looking at it (!) is to think of it in terms of "depth of field". With cameras, the depth of field is greatly influenced by the aperture. The smaller the aperture, the greater the depth of field (meaning the range of distances where objects are in focus).

The ultimate is the pinhole camera which has an almost infinite depth of field, but so little light makes it through the pinhole that it requires very long exposure times.

[MikeS]

A pinhole image can also appear to be slightly magnified.  I don't know whether this is a real effect or the brain enlarging the image because it now has something of greater clarity to work on.

[syhprum]

I my experience pinhole cameras work best at an "F" value of 300 making the aperture smaller does not seem to improve the resolution.

[Geezer]

I my experience pinhole cameras work best at an "F" value of 300 making the aperture smaller does not seem to improve the resolution.

I was thinking of a pinhole camera that does not have any lens.

[imatfaal]

The optimal size for the pinhole - assuming a very low thickness material is

Diameter = 1.9 √(fλ)

where f is the focal length (and before Gaesar goes on about pinhole cameras having no lens) this is the distance between the aperture and the screen.  Which for green light would give an f-stop of about 160 ish for a 5cm focal distance

As the f number is f/D and D is related to the sqrt of f then the optimal f stop varies with focal length.  A little maths shows that at 16.6 cm the best f number is 300