Optics: What is the color of the object as seen from under water?

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

[/B]
Since wavelength of light reduces on entering
water , then the wavelength of light entering the eyes of diver is less than the wavelength of green light .

Out of the given options , option B) i.e blue color is the only one with wavelength less than green .

But this is not the correct option .

What is the mistake ?

 

[Drakkith]

Does the light exit the water and immediately hit your retina?

 

[Jahnavi]

Does the light exit the water and immediately hit your retina?

Exit or enter ?

 

[Drakkith]

Exit or enter ?

Exit. What's between your retina and the water?

 

[Jahnavi]

Sorry . I am not understanding you .

Light from the green object enters the water , gets refracted and enters the eyes of diver . Isn't it ?

Why are you emphasizing on light exiting water ?

 

[cnh1995]

Exit. What's between your retina and the water?

I think the diver is inside the water and the green object is outside the water. The diver is looking at the green object.

I am no expert here, but dividing the wavelength of green light by the refractive index of water (1.33) gives a wavelength below 400 nm and the visible range is 400-700 nm.

 

[Drakkith]

I think the diver is inside the water and the green object is outside the water.

Whether the diver and the object are immersed in the same medium makes no difference. Otherwise we would experience drastic color changes viewing things in a fish tank, in a pool, etc.

 

[Drakkith]

Sorry . I am not understanding you .

Light from the green object enters the water , gets refracted and enters the eyes of diver . Isn't it ?

Why are you emphasizing on light exiting water ?

If the light is entering your eye, it has to exit the water, right? What is your eye composed of?

 

[Jahnavi]

If the light is entering your eye, it has to exit the water, right?

Why ?

We see an object when the light rays originated/reflected from that object enter our eyes .That's it .

Where is the point of light exiting the water ?

I might be missing something very fundamental .

 

[Jahnavi]

Are you suggesting that light exiting the water enters air somewhere before entering the eyes ?

 

[jedishrfu]

I'd say it would be green still.

The reasoning is that the frequency of the photons doesn't change as it traverses the water and into your eye hence you still see it as green.

 

[Jahnavi]

I'd say it would be green still.

The reasoning is that the frequency of the photons doesn't change as it traverses the water and into your eye hence you still see it as green.

But colour of an object is determined by the wavelength of light not the frequency ?

 

[jedishrfu]

But they asked what you will see and photoreceptors measure photon energy ($E = h * \nu$), right?

https://en.wikipedia.org/wiki/Photoreceptor_cell

 

[Drakkith]

Why ?

We see an object when the light rays originated/reflected from that object enter our eyes .That's it .

Where is the point of light exiting the water ?

I might be missing something very fundamental .

Prior to hitting your retina, the light has to proceed through the cornea, the lens, and finally the vitreous humour, which is what the retina is in. All of which are their own optical mediums. Does it matter whether the light originates in air, water, or some other medium if it all ends up in the same medium in the end?

 

[Jahnavi]

Prior to hitting your retina, the light has to proceed through the cornea, the lens, and finally the vitreous humour, which is what the retina is in. All of which are their own optical mediums. Does it matter whether the light originates in air, water, or some other medium if it all ends up in the same medium in the end?

This is what I was saying in post 10 .

But where is air just before the light reaches the retina ?

Light originated in air and just before it reaches retina , it traverses through vitreous humour .

It the object were to look green to the diver , it has to enter air before it reaches retina .

Does this make sense ?

 

[Jahnavi]

But they asked what you will see and photoreceptors measure photon energy ($E = h * \nu$), right?

https://en.wikipedia.org/wiki/Photoreceptor_cell

OK . I have little idea about this .

 

[Drakkith]

But where is air just before the light reaches the retina ?

There is none.

Light originated in air and just before it reaches retina , it traverses through vitreous humour .

It the object were to look green to the diver , it has to enter air before it reaches retina .

Does this make sense ?

No, as there is no air inside your eye, nor is any required to see the correct color. The wavelength of green light, when it strikes the retina, is not 525 nm. It has been reduced because the refractive index of the vitreous humour is greater than 1. And this has always been the case for your whole life, regardless of whether you're underwater or not. When we talk about the wavelength of a color, we are talking about the wavelength of that light as if it was traveling in a vacuum, not when it is inside the eye. The real wavelength at your retina is always smaller.

 

[jedishrfu]

I think the confusion is because we define colors using wavelengths but the eye's photoreceptors are sensitive to photon energy which causes electrons to be absorbed in the receptor proteins.

https://en.wikipedia.org/wiki/Spectral_sensitivity

 

[Jahnavi]

No, as there is no air inside your eye, nor is any required to see the correct color. The wavelength of green light, when it strikes the retina, is not 525 nm. It has been reduced because the refractive index of the vitreous humour is greater than 1. And this has always been the case for your whole life, regardless of whether you're underwater or not. When we talk about the wavelength of a color, we are talking about the wavelength of that light as if it was traveling in a vacuum, not when it is inside the eye. The real wavelength at your retina is always smaller.

To a person in the same medium as the object , the object looks green .

To a person under water the object looks green .

Does this mean , colour of an object as perceived by eyes does not depend on wavelength of light originated from object ?

 

[Drakkith]

To a person in the same medium as the object , the object looks green .

To a person under water the object looks green .

Does this mean , colour of an object as perceived by eyes does not depend on wavelength of light originated from object ?

The simple answer is yes, but as others have pointed out, we would also need to talk about photons, energy, and frequency, which would greatly complicate things.

 

[Jahnavi]

But they asked what you will see and photoreceptors measure photon energy ($E = h * \nu$), right?

https://en.wikipedia.org/wiki/Photoreceptor_cell

I think the confusion is because we define colors using wavelengths but the eye's photoreceptors are sensitive to photon energy which causes electrons to be absorbed in the receptor proteins.

https://en.wikipedia.org/wiki/Spectral_sensitivity

If colours as perceived by eyes do not depend on wavelength , then how do we see the sparkling of a diamond or a rainbow ?

@haruspex

 

[Jahnavi]

@jedishrfu , please see https://en.m.wikipedia.org/wiki/Color_vision

 

[Drakkith]

If colours as perceived by eyes do not depend on wavelength , then how do we see the sparkling of a diamond or a rainbow ?

@haruspex

Frequency and wavelength are directly related to each other. The shorter the wavelength, the higher the frequency, just like any type of wave. Nothing anyone has said here is contradictory in any way. What Jedi was saying about frequency being important and not wavelength is part of the "complications" I mentioned earlier.

 

[Jahnavi]

Frequency and wavelength are directly related to each other. The shorter the wavelength, the higher the frequency, just like any type of wave.

You are comparing lights of different wavelengths traveling in the same medium .

This is not the case in OP .

For a monochromatic light , the frequency of light doesn't change as it travels from one medium to other .

In the problem given , the frequency of light originated from the object doesn't change as it enters water . Speed and wavelength changes .

 

[Charles Link]

The eye basically responds to the frequency that hits it. It does not make a measurement of the wavelength of the light in the medium that it is traveling through that it appears to come from.

 

[jedishrfu]

So I'm guessing you got this question wrong and you are trying to argue with the teacher using the wavelength notion.

The problem here is that the light ray has traversed through two mediums to get to your eyes and while its true the wavelength has shortened in the water medium, its also true that its speed has diminished as well.

Now the tricky part here is to realize that the conservation of energy is at work so that photons traveling in air and then in water will retain the same energy and hence the same frequency across the transition. Photons of the same energy excite the photoreceptors in the same way hence giving you the sense of seeing the same color. This means that you can't use wavelength as a means to describe what the eye sees but rather the energy or the frequency of the photon as to what the eye sees.

I like to use the energy of the photon because it relates to the excitation of some electron in the photoreceptor protein that triggers the sense of the color we are seeing. Its more of the quantum mechanical view of the process.

 

[Jahnavi]

Don't you think it is easy to get the wrong notion considering the fact that colours are related to wavelengths , and wavelengths change as the medium changes ?

You did acknowledge this in post 18 .

 

[jedishrfu]

One last point I forgot to mention is why green was chosen for the problem. The question author no doubt chose green because green and blue photons can penetrate the water column the deepest whereas other colors are attenuated ie disappear as you go deeper.

This means that a multicolored object would lose some of its color depending on depth. One such example would be viewing the American flag (red/white/blue color pattern) from underwater as you got deeper the red would disappear and appear as black. The white which reflects all light would become blue meaning the flag would look like shades of black and blue stripes and stars and finally it would all just be blackness when no more light can penetrate the depth.

https://oceanservice.noaa.gov/facts/light_travel.html

The other part of the question "diminished wavelength" while true was designed to mislead the student who most probably is thinking of color in terms of wavelength.

In truth, I got fooled by this too and after talking it over with a colleague understood the nature of the question and my confusion.

Thanks for bringing this question to PF, I think we all learned something here.

 

[Drakkith]

Don't you think it is easy to get the wrong notion considering the fact that colours are related to wavelengths , and wavelengths change as the medium changes ?

Yes, it's easy to misunderstand since it color is usually given in terms of a wavelength instead of a frequency or an energy. The latter two never change.

 

[Jahnavi]

I agree

Thanks to all who have participated in this thread .

 

[ehild]

As @jedishrfu pointed out, the color of light depends on the energy of the photons, E=hf, that is, on frequency f. As it is a very high number, and old spectrometers measured light intensity in terms of wavelength, we say that visible light is between 400 and 800 nm of vacuum wavelength, (λ₀=c/f) The frequency of light does not change at refraction. The wavelength changes, but the color does not.