# How does light bend around my finger tip?

When I close one eye and put the tip of my finger near my open eye, it seems as if the light from the background image bends around my finger slightly, warping the image near the edges of my blurry finger tip.

What causes this? Is it the heat from my finger that bends the light? Or the minuscule gravity that the mass in my finger exerts? (I don't think so.) Is this some kind of diffraction?

For all the people asking, I made another photo. This time the backdrop is a grid I have on my screen (due to lack of grid paper). You see the grid deform ever so slightly near the top of my finger. Here's the setup:

Note that these distances are arbitrary. It worked just as well with my finger closer to the camera, but this happens to be the situation that I measured.

Here are some photos of the side of a 2 mm thick flat opaque plastic object, at different aperture sizes. Especially notice how the grid fails to line up in the bottom two photos.

OK, it seems that user21820 is right; this effect is caused by both the foreground and the background objects being out of focus, and occurs in areas where the foreground object (your finger) partially occludes the background, so that only some of the light rays reaching your eye from the background are blocked by the foreground obstacle.

To see why this happens, take a look at this diagram:

The black dot is a distant object, and the dashed lines depict light rays emerging from it and hitting the lens, which refocuses them to form an image on a receptor surface (the retina in your eye, or the sensor in your camera). However, since the lens is slightly out of focus, the light rays don't converge exactly on the receptor plane, and so the image appears blurred.

What's important to realize is that each part of the blurred image is formed by a separate light ray passing through a different part of the lens (and of the intervening space). If we insert an obstacle between the object and the lens that blocks only some of those rays, those parts of the image disappear!

This has two effects: first, the image of the background object appears sharper, because the obstacle effectively reduces the aperture of the lens. However, it also shifts the center of the aperture, and thus of the resulting image, to one side.

The direction in which the blurred image shifts depends on whether the lens is focused a little bit too close or a little bit too far. If the focus is too close, as in the diagrams above, the image will appear shifted away from the obstacle. (Remember that the lens inverts the image, so the image of the obstacle itself would appear above the image of the dot in the diagram!) Conversely, if the focus is too far, the background object will appear to shift closer to the obstacle.

Once you know the cause, it's not hard to recreate this effect in any 3D rendering program that supports realistic focal blur. I used POV-Ray, because I happen to be familiar with it:

Above, you can see two renderings of a classic computer graphics scene: a yellow sphere in front of a grid plane. The first image is rendered with a narrow aperture, showing both the grid and the sphere in sharp detail, while the second one is rendered with a wide aperture, but with the grid still perfectly in focus. In neither case does the effect occur, since the background is in focus.

Things change, however, once the focus is moved slightly. In the first image below, the camera is focused slightly in front of the background plane, while in the second image, it is focused slightly behind the plane:

You can clearly see that, with the focus between the grid and the sphere, the grid lines close to the sphere appear shifted away from it, while with the focus behind the grid plane, the grid lines shift towards the sphere.

Moving the camera focus further away from the background plane makes the effect even stronger:

You can also clearly see the lines getting sharper near the sphere, as well as bending, because part of the blurred image is blocked by the sphere.

I can even re-create the broken line effect in your photos by replacing the sphere with a narrow cylinder:

To recap: This effect is caused by the background being (slightly) out of focus, and by the foreground object effectively occluding part of the camera/eye aperture, causing the effective aperture (and thus the resulting image) to be shifted. It is not caused by:

• Diffraction: As shown by the computer renderings above (which are created using ray tracing, and therefore do not model any diffraction effects), this effect is fully explained by classical ray optics. In any case, diffraction cannot explain the background images shifting towards the obstacle when the focus is behind the background plane.

• Reflection: Again, no reflection of the background from the obstacle surface is required to explain this effect. In fact, in the computer renderings above, the yellow sphere/cylinder does not reflect the background grid at all. (The surfaces have no specular reflection component, and no indirect diffuse illumination effects are included in the lighting model.)

• Optical illusion: The fact that this is not a perceptual illusion should be obvious from the fact that the effect can be photographed, and the distortion measured from the photos, but the fact that it can also be reproduced by computer rendering further confirms this.

Addendum: Just to check, I went and replicated the renderings above using my old DSLR camera (and an LCD monitor, a yellow plastic spice jar cap, and some thread to hang it from):

The first photo above has the camera focus behind the screen; the second one has it in front of the screen. The first photo below shows what the scene looks like with the screen in focus (or as close as I could get it with manual focus adjustment). Finally, the crappy cellphone camera picture below (second) shows the setup used to take the other three photos.

Addendum 2: Before the comments below were cleaned out, there was some discussion there about the usefulness of this phenomenon as a quick self-diagnostic test for myopia (nearsightedness).

While I Am Not An Opthalmologist, it does appear that, if you experience this effect with your naked eye, while trying to keep the background in focus, then you may have some degree of myopia or some other visual defect, and may want to get an eye exam.

(Of course, even if you don't, getting one every few years or so isn't a bad idea, anyway. Mild myopia, up to the point where it becomes severe enough to substantially interfere with your daily life, can be surprisingly hard to self-diagnose otherwise, since it typically appears slowly and, with nothing to compare your vision to, you just get used to distant objects looking a bit blurry. After all, to some extent that's true for everyone; only the distance varies.)

In fact, with my mild (about −1 dpt) myopia, I can personally confirm that, without my glasses, I can easily see both the bending effect and the sharpening of background features when I move my finger in front of my eye. I can even see a hint of astigmatism (which I know I have; my glasses have some cylindrical correction to fix it) in the fact that, in some orientations, I can see the background features bending not just away from my finger, but also slightly sideways. With my glasses on, these effects almost but not quite disappear, suggesting that my current prescription may be just a little bit off.

• Isn't parallax? Oct 20, 2017 at 16:51
• Your explanation has been made into an educational video on the It's Okay To Be Smart YouTube-channel: youtu.be/xnrXwpE2pMg Apr 4, 2018 at 21:58

Contrary to some of the answers people have posted on Yahoo Answers (like here and here) and other places, this is not caused by diffraction.

To show this, note that the bending effect can roughly be modeled as the diffraction pattern due to light incident on the edges of an opaque object. As explained by Rod Vance, the intensity profile on a screen at height $x$ due to a flat object a distance $d$ from the screen is given by $$I(x)\propto\left| C\left(\sqrt{\frac{k}{2d}} x\right)+i S\left(\sqrt{\frac{k}{2d}} x\right)+\left(\frac{1}{2}+\frac{i}{2}\right)\right|^2$$ where $C$ and $S$ are the FresnelC and FresnelS functions, and $k=2\pi/\lambda$ is the wavenumber of the light.

Using $d=5\text{cm},\lambda=600\text{nm}$, this gives

This indicates that there's a spread of roughly $0.05\text{mm}$ to $0.1\text{mm}$. This is a very small distance, roughly the same as the thickness of a sheet of paper, and far smaller than the quite visible sag towards the finger present in the $2^\text{nd}$ blue line on the paper background. So while diffraction may play a small role, it seems doubtful that it's the dominant role.

Additional evidence against it being due to diffraction come from considering chromatic effects. The bending is strongly $\lambda$-dependent, with red light bent more strongly than blue light. If diffraction were the primary phenomenon responsible, you'd expect to see a rainbow-effect at the edges of your finger, in which the light from the paper gets bent by different angles depending on wavelength. However, this is not observed.

Also (and probably the most important point!), as rob pointed out in his answer, diffraction would cause the blue lines behind the finger to appear to bend upwards, but instead they appear to bend downwards.

I'd guess that some sort of geometric factors (perhaps with the camera, lenses, etc?) play the primary role here, but I'll await the judgement of people who know more about optics than I do.

• Actually when I try this with my finger I can see chromatic abberation May 3, 2014 at 15:48
• @BrianFunt In light of the accepted explanation I'm very curious to know whether you can reproduce or explain the chromatic aberration you observed.
– rob
May 6, 2014 at 15:46
• @rob If I take a piece of card and hold it against a bright background such as the sky, then focussing on the top edge of the card and bringing my finger up, the edge of the card becomes slightly blurred and yellowish. If I look at the bottom edge of the card and bring my finger up, the edge becomes bluish this time. Interestingly, if I really try to focus on the card so that the 'bending' effect isn't noticeable (as expected from the answer), the chromatic aberration(?) remains visible. May 6, 2014 at 16:31
• I have attempted without avail to photograph this, trying various apertures, over and under exposing, and various focal lengths. Although it has just occurred to me that I didn't try it with the card out of focus... May 6, 2014 at 16:56
• @BrianFunt: This does not actually seem all that surprising: the human eye has some chromatic aberration, which causes different colors to be in slightly different focus, and thus to experience the bending effect in different amounts. I suspect that photographing this effect would be easiest with a really low-quality camera lens with significant chromatic aberration; a good achromatic lens will defeat your efforts here. May 8, 2014 at 12:26

Haha when I was young I thought that this effect was due to gravity, which is of course too weak for tiny objects to be observable. But it turns out that it is neither refraction nor diffraction nor parallax error. Instead it is due to having the wrong focus. If you are short-sighted like I am, then when looking at a far object each point will generate a circular disk image on your retina instead of a sharp point. When you move the edge of any object near your eye and it blocks part of the pupil, then the image generated on your retina will no longer be a full disk, hence the image appears to shift away from the edge. This explains your four later grid images. Notice that the rest of the grid is never in sharp focus, but the region near the edge of the occluding object is sharper, which is because those points generated less than a full disk on the camera sensor plane. As for your earlier images, they were due to the focus being beyond the object you were looking at. As before, each point would result in a disk image on your retina, but inverted. Thus when another object blocks part of your pupil, the image appears to shift towards the edge instead of away from it.

Edited: Ilmari Karonen has posted a complete and convincing answer to this question. I'm leaving this answer up, despite downvotes, because it contained useful hints: the effect was inconsistent with diffraction of light around obstructions, and had something squishy to do with imperfect focus in a non-ideal optical system.

I think it's interesting that distorted part of the line is nearer to your fingertip than the undistorted part. That suggests it isn't diffraction. If diffraction were permitting light from the blue line to travel over the top of your fingertip, those rays would enter your eye with a slight downward angle, compared to the undeflected light on either side. That would make the image of the distorted part of the line appear slightly higher. If you have light reflecting from your fingertip, on the other hand, you'll see the line bend down. Here's a cartoon:

This raises the question of why you don't see both a direct and reflected image; I suspect that the angular separation is small enough that the camera's focus can merge the two images, but I don't have a good model for that yet.

• I think you're right that it's not refraction. I've noticed this before but hadn't properly thought about it. I suspect that it is due to the camera or eye's finite aperture. A cone of light leaving a point on the background grid will hit the lens and be focussed down to converge at a spot on to the sensor. The finger (which is out of focus) blocks some of the light cone, but not all of it (as you can see form the blurry shadowing in the effected region). I think the obstruction somehow causes the point of convergence to bend out of place. May 3, 2014 at 19:09
• A similar feeling effect for anyone with even slightly out of focus vision: Make a finger pin-hole (or use a piece of paper), hold it to close to your eye and look through it. You can sharpen up your vision & improve contrast, though you lose brightness. Glasses for free, if you like. May 3, 2014 at 19:22
• Oh – "not refraction" should have said "not diffraction", although I don't think it's refraction either. May 3, 2014 at 19:57

It seems to me this is actually a case of parallax, for the most part. Your retina and camera CCD are not point sinks. They are an array of point sinks. If you sum the point sinks (photo receptors) over the surface of each of these imaging sensors you will achieve this exact effect.
You can demonstrate this by holding your finger farther from your face (to account for the larger distance between sensors), focus on something in the background (as required with your one eye example), and mentally (or digitally with a camera) overlaying those two images.
You will get a solid overlap where both eyes see the same image and a fuzzy edge where the view is different.
Try holding your finger even closer to you face, the blur around it gets larger because it's parallax and the effect is increased with smaller distances.

There are many things happening which could have an influence on what you see (what kinds of distortion happen). Some have been touched on (or more fully discussed) in other answers, so I won't go into detail:

1. Aperture and focus effects
2. Optical system aberrations (low quality lens in the eye or camera)
3. Diffraction around an object
4. Your skin (in fact, your whole finger except for the bone) isn't quite opaque -- a little light gets through it, being bent in the process. Using an object like a piece of sheet metal or pencil would avoid this.
5. Your finger is likely a bit warmer than the surrounding air. Warmer air is less dense, and so would slightly bend light away from your finger. There may also be convective currents affecting the light further away from the finger, depending on orientation. Using an object that is at the same temperature as the air would help here.
6. Light being bent by the mass of your finger (a very, very tiny effect that will probably never be measurable. Read about the measurement of a star's light being bent by the Sun, during a 1919 solar eclipse, that was one of the first confirmations of Einstein's General Theory of Relativity. It was a quite small angle.)

All of these things (and possibly more that I can't think of at the moment), in roughly descending order, are affecting the image and have to be accounted for.