How does light, which is an electromagnetic wave, carry information? We see an object when light from a source strikes the object and then reaches our eyes. How does light, which is an electromagnetic wave, gets encoded with the information about the object? Do the individual photons get encoded with this information or is it the wave nature of light that gets modified to carry information about the object?
Also, if light hits an object and then another on the way to our eyes, does it only carry information from the very last interaction it had? How is the information due to all previous interactions erased (if it is indeed)?
 A: I think that trying to think in terms of light "getting encoded with information" is a confusing and excessively complicated way of thinking about things.
Suppose I'm standing next to a window, and there's a lamp on the other side of the window. When light from the lamp encounters the glass, what happens? If you wanted, you could describe what happens like this:
The light becomes encoded with the information that the matter in that region of space is transparent.
But that would be a severely overcomplicated way of describing what happens. A much simpler description of what happens is this:
The light passes through the glass.
In the vast majority of everyday situations, when light encounters an object, it passes through the object (transmission), bounces off the object (reflection), or is destroyed (absorption). It's as simple as that; the photons don't "get encoded with information."
When a beam of light strikes, say, a word written on a piece of paper, all that happens is that some of the light gets reflected and some of it does not.
A: Let me first deviate to radio&television: a radio wave with constant frequency does not carry information, since it is absolutely predictable on the basis of a few parameters: its amplitude, its frequency and its initial phase:
$$
X(t) = A\cos(\omega t +\varphi)
$$
The information is encoded into the wave by modulating these parameters, i.e. by changing them in time. This is how we get amplitude modulation (AM), frequency modulation (FM), and phase modulation (the very AM/FM that one sees on radios). The rate of this modulation is usually quite low, compared to the carrying frequency $\omega$ - without this high frequency the signal would never propagate at long distances.
When it comes to optical fiber, the above mentioned modulation techniques are impractical due to extremely high light frequencies (as compared to radio frequencies), so on resorts to numerical encoding of $0/1$ when the light is off/on. This could be thought of as a kind of amplitude modulation.
Finally, coming back to the natural light, we see that it similarly encodes information, although perhaps in even more ways: in its frequency - more precisely in the spectrum of its frequencies, in its direction, in its phase, etc. Btw, the difference between conventional and holographic images is that one does not record the phase, while the other does.
A: Light may carry information defined by which frequencies of the light spectrum it has. For example, the colour of an object is information carried by light. White light from the sun is actually many different wavelengths combined to create "the colour white". These wavelengths can teach us about:

*

*What object it reflected off of


*What created this light


*What things the light had to go through before reaching us.
A: Imagine an alien drops a transparent artifact nearby.  Not knowing what it is, or whether it's dangerous, you decide not to try to walk up to it and touch it.  All you know is that you can see through it, and thus, you don't really know what its outline looks like.  However, you have several children and lots of plastic balls.  So you give each child a bucket, and ask them to walk in a big circle around the artifact, and throw balls at it.  As they do so, you observe the balls bouncing off the artifact in a particular pattern which gives away its overall shape, more or less.
Now, this is a rather imperfect analogy, because the balls respond to gravity quite a bit, and you can see balls that don't bounce towards your eyeball.  And yet, this is, on a very gross level, how vision works.  The plastic balls are a "poor man's photon", and the children are crude "light sources".
Imagine that the alien drops multiple artifacts, some of which are actually close to together.  Now, if a child throws a ball that bounces off one artifact, hits another, and bounces again, you will get information about both bounces.  But if the child happens to be at an angle where you don't notice the first bounce because the ball is moving directly towards or away from you, then all you will really see is the final trajectory of the ball.  More importantly, if you could freeze time and look at all the balls in flight, along with a short momentum vector, would you be able to answer the question: "Which artifact did this ball bounce off of?" you could most likely guess by looking at the vectors and seeing where they converge.  But if you had to answer the question: "What other artifacts did this ball bounce off of?" I think you would be hard-pressed to answer this question at all, because the final direction of the ball doesn't give you this information.
In the same way, when a photon comes into your eyeball and is detected by your retina, there is no "history" of its path encoded into the photon.  But think about what the world would look like if you could see the "photonic history".  Whenever you look at a scene, you would not only see the traditional image, but you would also see all shiny objects in the scene superimposed on everything else which is visible, all the way back to the light sources.  So if there's a lamp nearby which illuminates most of the scene, you would see the lamp in every part of the scene, which would be pretty confusing at best.
A: You talk about light as if it were a person carrying a clip board writing down things on its way to you. It is a physical phenomenon that gets affected as it propagates.
Depending on the various processes that it goes through before it reaches your eye, its amplitude,polarisation, frequency (or wavelength), pulse time etc. get affected from which we can infer what it must have gone through and get to know of the object it must have reflected off or gone through or originated from.
If the frequency is changed, the photon is said to have a different energy from $E=h\nu$. Since light has both particle and wavelike properties, depending on the situation we are in, we can equally talk about $k=\frac{2 \pi \nu}{c}$
Consider these examples:

*

*Say you have a pocket laser source. You shine it on two walls, one at 500 m and one at 1 km. The light travels for more time to get back to you from the second wall. Here, the light is unaffected but only the time is recorded. If you did not know the distance the walls were from you, now you can calculate the distance the walls are at. This is information


*Leaves are green. This means that they reflect green light and absorb all the other colours that are present in the sunlight. When you go outside and can "see" a leaf, it is information. Now, the frequencies of a light have been partly affected.


*You see stars at night. Light has travelled for many years and the photons have hit your eye. Now you know how the star looked some few years ago. (the light from the nearest star takes around 4.5 years to come to you). Thus, information on the star's position is being carried, along with it's temperature. The wavelength of the light reaching you is carrying information.


*Light from objects are also "doppler shifted" : the police use this effect to get the information - the speed of the car that they shine the radar gun on. The frequency is actually changed in this process. This frequency change is carrying information.
A: When you receive a beam of light, you can measure five things:

*

*the direction it came from

*its wavelength distribution (roughly, its color)

*its intensity (how bright it is)

*its polarization (an aspect of light we typically can't see)

*what time it arrived (or how aspects 1–4 change in time)

This is all the information you have. When our eyes receive light, we measure the direction it came from and how bright it is. We also sample three parts of its wavelength distribution (color) and know what time we saw it relative to other events. Our brain processes this information based on our past experience and instincts to tell us that there is a truck coming toward us and that we should get out of the way. Other devices we have built similarly measure some of the aspects listed above to infer something about the universe.
For example, the wavelength distribution (color) of a star can tell us how hot it is. In a sense, the light carries the information about what the temperature of the star is. However, like for the car, we need some background information about how stars work to interpret that information. The interpretation is an important part of using those 5 pieces of information. I can show you a television screen with an image of a truck and maybe even make you believe that there's a truck coming toward you. Similarly, I could design a lamp that has the wavelength distribution of a star of a particular temperature, even if this lamp is not as hot as star.
*Numbers 2 and 5 are related, although they can be considered independent if the frequency of light is on a much shorter time scale than the changes in time in number 5.
A: When a photon hit the retina, it only has two pieces of information:
Its wave length and its position/direction.  That is all.
But it is not alone.  We are bombarded with billions of photons every second and the pattern these photons make is where the information is hiding.
And we have a brain that is pretty good at figuring out these patterns.
Let's say a video projector projects a movie on an blue wall with a picture on it.  You are looking at the result.
If you look at one individual photon, it can be reflected off the wall or picture, or it can be absorbed.  An absorbed photon has no information for us, and the reflected photon only has its wave length and position.
The information on the position of the projector is completely lost. But the pattern of the movie is still there.
What happens when this pattern hits the blue wall is that most of the blue photons are reflected but fewer of the other photons are.  Again, this is only apparent when you look at the pattern made from many photons.
And the picture will have areas with different colours which each reflect or absorb photons in their own way.  In this way it adds its own pattern to the steam of photons.
The light that eventually hits your eye is a mixture of the movie pattern, the picture pattern and the colour of the wall.  This can be confusing, but for the most part your very clever brain can figure it out.
A: Your other questions have been beautifully answered by other users and I will try to explain the second part of your question.

Also if light hits an object and then another one on the way to our eyes, does it only carry information from the very last interaction it had ? Where does the information due to all previous interactions go (if it is indeed) ?

For this to understand take an  example. Suppose you have a book , a white light source and you keep both of them in a huge compartment where there is no air (i.e. complete vacuum) . The book is adjusted in such a way that it is visible to you when the light is turned on. Now if the light source glows, the photons strike the electrons in the book and then the book allows or releases photons of certain frequency only  (which come to us and we see them as a coloured object). So light from the book directly came to your eyes and there was nothing in the middle to reinteract.
Now suppose you allowed air to come in the compartment .
What is the colour of the book ?
Of course the same one which you saw when there was complete vacuum.  The photons from the book are still interacting with the molecules of air but the information of the book (i.e. its colour) didn't change.
Why did this occur ?
The explanation for this is the same as for why things are transparent and certainly there are brilliant people who can explain this better than I.
Now in place of air what if you keep a green filter glass in front of your eye.
Now
Do you see the object now ?
The answer to this will depend upon the nature of the book i.e. its composition (the atoms constituting it). Depending upon the frequency of the photon coming from the book, the book will be either visible or not.
So first of all there is nothing like being encoded . The frequency or the wavelength of the coming photon decides what you see . During interaction with any object , the frequency of the photons may or may not change and so you can't say definitely that the photon coming to your eyes is the same photon which hit that object from the main light source and so arguing about information's being erased or something else is useless.
For the reason behind transparency give
This video a try.
Hope it helps. 
A: 
How does light, which is an electromagnetic wave, gets encoded with
the information about the object?

There are several stages to this. Initially there has to be a light source emitting photons. This can be the object itself, but is more likely to be a separate light source such as the sun or a light bulb, usually a 'white' or 'wide spectrum of wavelengths' light source.
Photons from the light source hit the viewed object whereupon some of the wavelengths are absorbed and some re-emitted (reflected), depending on the colour of the object. These re-emitted (reflected) photons are then imaged by the eye lens and reach a sensing cell (rods or cones) on your retina. Your brain knows that each rod or cone can only get stimulated by photons entering your eye lens at a unique angle. In this way the brain builds up a map of the scene.
What's more, the 3 colour receptors in the retina can also detect which wavelengths got absorbed and compares it to the overall level from all your colour receptors. In ths way the brain is able to determine the colour of the object which sent the photons in at each angle. - i.e. the colour of each point in the scene.

Also, if light hits an object and then another on the way to our eyes, does it only carry information from the very last interaction it had?

Each prior interaction can vary the relative wavelength absorption (colour), intensity, and direction of the reflected light. Other factors such as polarisation can also be affected, but the eye can't detect that directly.
A: Assume Light is a being.
Light doesn't carry information. All it does is, just pass through, if the object it hits, allows it to pass through or it gets reflected back.
Example 1 :
Infrared Laser in Scanning barcodes.
Barcodes are nothing but alphanumerics shrinked in size. When infrared laser is allowed to hit it. Each letter in that alphanumeric information lets the laser pass through the area, only surrounding its shape but not the light that hit on the shape/surface ( gets blocked and reflects back ) paving way for the information detection.
Example 2:
Kepler-1649c - Transit method - Dips in brightness
The Method used to collect data over years to discover an earth like planet. For more info, check this link
A: In a pinhole camera, the photons/waves strike a scene, self-modulate, and then organize contiguously into a 2D image.  Where is the template stored for the image if the brain is a 1d processor?
The question is concerned with the nature of informational dimension vs. spatial dimension.  The material world cannot account for the phenomenon of spatial dimension because the brain is a bit processor, and bits have no dimension.
For years most held a mind/brain duality viewpoint, including Leibniz, Des Cartes, Newton, and Tesla.
In modern day, science has deviated from this assumption.
There is no dimensionality to thoughts if they are limited to the brain only.  Close your eyes and envision a cube.  It does not exist as described as 8 orthogonal corners with infinite Euclidean points.
It’s because the cube doesn’t exist in the brain as described.
Knowing, consciousness, etc. is a metaphysical event.  The scientists above knew this.  Light is perceived and  its self-organizing properties known via consciousness.  It self-encodes based on the substrate it interacts with and confers this info to other substrates even in a stochastic (to us) universe.
The same question can apply to audio.  Countless waves in a cathedral performance can arrive at a single diaphragm and the diaphragm only resonates 1D voltage information at each vibration.  Yet within these vibrations are countless “subvibrations” of timbres viewable via fourier spectography that shows the 3D audio data encoded. Where is all the data?  Every last overtone, timbre, reverb stored in strings of 0’s and 1’s that represent “layers” of data not directly in those binaries. And then how can a speaker reproduce all of it by only “hearing“ one wave?  Because the nature of information goes way deeper than what meets the eye.
