Interference Patterns on an iPod Screen
- 8:24 am |
My daughter was pretty annoyed with her iPod case (with a screen protector). It had this interference pattern on it – here is a vine version.
She asked how to get rid of the pattern, I just thought it was cool.
What is this pattern?
This is called a thin film interference pattern. Basically, some colors of light constructively interfere while other colors cancel. It is caused by a very thin layer in between the iPod glass and the screen protector. How do you remove the pattern? I think the only way to “fix” this is by taking the screen protector off and then putting it back on. This should “reset” the screen protector so that it doesn’t have this spot that is very close to the iPod glass.
What is interference?
I guess there is another question: what is interference? Any wave can have interference. Suppose I take a string and place it on the ground. Next I give one end of the rope a quick shake that makes a pulse travel down the length of the string. Now, what if someone did the same thing on the other end of the string? Two things could happen when these two string pulses meet. They could either add together to make a larger pulse, or they could cancel.
Of course light isn’t a wave on a string. It is a wave though. It’s an electromagnetic wave. This means that it is a propagation of a changing electric and magnetic field. What matters in this case is the wavelength. Different wavelengths of light are detected and interpreted by our eyes (and brains) as different colors. Violet is the shortest wavelength we can see and red is the longest.
Here is a scale representation of red, green and blue light.
Light doesn’t have to be a cosine or sine wave – but it is just easier to draw it that way. But you can see that the red light has a longer wavelength than the blue. If you were to actually measure these wavelengths you would find the red to be about 650 nanometers (nm), green at about 525 nm and violet at around 400 nm. I say “about” because there are many shades of “red”.
Ok, let’s say I have some flashlight that produces just these three wavelengths of light. Now suppose that I have a second flashlight that is shifted over just a bit but produces the same three colors. Here is what that might look like.
Here the second source is shifted over by an amount equal to the wavelength of the green light. So, for the green light, the two waves are right on top of each other and constructively interfere. What about the other two colors? For both the red and the blue, the wavelengths don’t quite cancel and don’t quite add up.
Oh, there is one more important thing to consider. What happens when light enters a different material – like glass or oil? We can characterize these materials with an index of refraction (n). This is a unitless number that tells us the ratio of the speed of light in a vacuum to the speed of light in that material. When a red light enters glass, the wavelength becomes shorter.
When light goes from one material to another, it can both reflect off the material and go through the material. Usually, both of these cases happen at the same time. Just imagine looking through a glass window. You can see that light goes through, but some light is also reflected. If the light reflects off a material with a higher index of refraction, the phase of the wave shifts by half a wavelength.
There is a great string based analogy to this flipping wave reflection. Suppose that I send a wave down a string and the end of that string is tied to a pole. If the string can move up and down on the pole, the wave reflects back not “flipped”. If the string can not move, the wave flips when it is reflected.
Ok, I think we can go back to talking about the iPod screen now.
Interference with a screen protector
Let me start with a diagram showing a side view of an iPod screen along with a screen protector. Of course, this is not drawn to scale. I will also include some paths that light takes when reflecting off the screen.
When light gets to the back side of the screen cover, it takes two different paths. Path 1 reflects off the back of the cover and path 2 goes through the cover and then reflects off the iPod screen. The key is that these two paths have different lengths. Essentially, it is the same as the case above where one light source was moved forward a little bit.
Let’s get an expression for this path difference. How much farther does light in path 2 go compared to path 1? The light in path 2 has to go down a distance s and then back up a distance s. Also, there is a phase shift when the light reflects off the iPod screen (assuming that it has a higher index of refraction than air). Notice that path 1 does not have a phase shift for its reflection since air is on the other side. This puts the distance for path 2 at:
If this path difference is the same length as one wavelength then the light in the two paths will match up and constructively interfere making a brighter light. If the path difference is half a wavelength, the the two paths will exactly cancel. Actually, there are more solutions. You also get a bright interference if the path difference is 2 or 3 or 4 wavelengths. You get destructive interference if the path difference is 1.5, 2.5, 3.5 wavelengths.
Since the interference depends on the wavelength of the light, you can have one color constructively interfering while another color destructively interferes. This is why you get the different colors on the iPod screen. Oh, the technical term for this situation is call “Newton’s Rings“.
In my vine video above, you can see that the interference colors change as the angle of viewing changes. This is because there will be path length changes as the light enters the screen cover and the air gap at a different angle. Of course, different path lengths mean different wavelengths of light that constructively interfere.
Thin film interference
You may have seen another situation that is similar – oil on water. A little bit of oil on water will float on top of the water. The oil also spreads out to very thin levels. It gets so thin that light reflecting off the top surface and the the light going through the oil then reflecting off the water can have different path lengths on the order of a wavelength. You get the same kind of effect as above – it is slightly different, but you get the idea.
Remember, it’s all about path length difference. The original question might have been “how do I get rid of these colors on my iPod?” My best answer is to just take off the screen protector. My second best answer is to take off the screen protector and put it back on.
Maybe the best answer is actually just “forget about it”. Why? When you turn the iPod on, you don’t see this pattern. When light comes from the screen (and not reflected off the screen), it would have to pass through this air gap three times in order to have a different path length. Think of the screen facing up – the light would go up, reflect back down off the screen protector and then reflect off the actual iPod screen. This means that you don’t see this interference pattern when viewing light from the iPod – so who cares if it’s there when the iPod is off?