Red shifted reflection

[johnduff]

Question from a chemist for any physisist willing to answer.

 

There exists a device which I learned to call a "radiometer". The device consists of a paddlewheel supported in an evacuated sphere on low friction bearings such that the paddlewheel can spin about a verticle axis. The arms of the paddlewheel are mirrors, reflective on one surface, and absorbtive on the other surface. When exposed to a bright light (sun light, for example), the paddlewheel spins. The purpose of the device is to demonstrate ( to a physics class) that light carries momentum and energy. The demonstration is compelling.

 

My question is:

 

Where does the kinetic energy of the mirror come from?

 

The reflected light carries the same energy as the incident light (E = h f).

One might suppose that the reflected light would be red shifted (have less energy), but I have never heard that this was the case.

 

This question has been nagging me for years, and this seems to be a good place to ask it.

 

john duff :)

[UncleAl]

A radiometer will not work in hard vacuum. The dark side of the vane heats residual gas. Reaction force then propels the vanes. You will note the dark side provides thrust, not the mirror - direction of spin. If it were only light being absorbed or reflected, the mirror would have twice the momentum change as the absorber.

[Erasmus00]

Question from a chemist for any physisist willing to answer.

 

There exists a device which I learned to call a "radiometer". The device consists of a paddlewheel supported in an evacuated sphere on low friction bearings such that the paddlewheel can spin about a verticle axis. The arms of the paddlewheel are mirrors, reflective on one surface, and absorbtive on the other surface. When exposed to a bright light (sun light, for example), the paddlewheel spins. The purpose of the device is to demonstrate ( to a physics class) that light carries momentum and energy. The demonstration is compelling.

 

My question is:

 

Where does the kinetic energy of the mirror come from?

 

The reflected light carries the same energy as the incident light (E = h f).

One might suppose that the reflected light would be red shifted (have less energy), but I have never heard that this was the case.

 

This question has been nagging me for years, and this seems to be a good place to ask it.

 

john duff :)

 

 

It appears that the rotation isn't actually due to light pressure. This site might be helpful.

 

http://www.answers.com/topic/crookes-radiometer-2

 

But I do have another question for the forum, similar to the one above. Light strikes a reflective surface that is free to move. Conservation of momentum means that the reflective surface picks up some momentum when our light bounces off it. But conservation of energy then implies that the energy of the photon should, in fact, have diminished. Does this mean that reflected light does indeed red shift?

-Will

[Qfwfq]

Where does the kinetic energy of the mirror come from?

From the photons. If the paddlewheel is in a good vacuum the propulsion is simply due to the reflection. If there is gas then the absorbtive sides heat the gas more that the reflective sides, with a contrary effect, much like UA says except that he gets it somewhat backwards, ;) .

 

The reflected light carries the same energy as the incident light (E = h f).

One might suppose that the reflected light would be red shifted (have less energy),

Very slightly. The velocity of the paddles is a tiny fraction of that of light, so the redshift is tiny.

[johnduff]

UncleAl:

 

Thank you for your response.

 

Your answer attributing the spin to gas dynamics is one I have encountered before, and I accept your answer as true. But I'm afraid my choice of the radiometer was a bad illustration for the question I was trying to ask.

 

In place of the radiometer, consider a solar sail powered spaceship. The ship ( and sail ) gain momentum and energy from incident sunlight. Assuming the reflected light is not red shifted (which is apparently the case), where does the energy driving the ship come from?

[johnduff]

Eramus:

 

The question you ask at the end of your response to my original question is the one that has been bothering me. Your phrasing is better than mine, but I think we have the same question.

 

I will add that I don't think the reflected light is red shifted, making the question "Where does the kinetic energy of the mirror come from?" the question of interest.

 

Thanks for answering

John Duff

[C1ay]

See http://science.howstuffworks.com/solar-sail.htm

[johnduff]

[Qfwfq:. The velocity of the paddles is a tiny fraction of that of light, so the redshift is tiny.

 

The instantaneous velocity of the reflecting mirror does cause a red shift or a blue shift, depending on whether the mirror is approaching or receding from the light source. This is standard Doppler type effect and is well understood. But consider the case where the mirrors velocity is zero. Light applies a force to the mirror, causing the mirror to move, gain momentum, and kinetic energy. My question is, "Where does the energy come from?"

 

It is my understanding that reflected light is not red shifted (from a stationary mirror). so where does the energy come from that causes the mirror to move?

 

Thank you for your response;

 

John Duff

[Erasmus00]

The instantaneous velocity of the reflecting mirror does cause a red shift or a blue shift, depending on whether the mirror is approaching or receding from the light source. This is standard Doppler type effect and is well understood. But consider the case where the mirrors velocity is zero. Light applies a force to the mirror, causing the mirror to move, gain momentum, and kinetic energy. My question is, "Where does the energy come from?"

 

It is my understanding that reflected light is not red shifted (from a stationary mirror). so where does the energy come from that causes the mirror to move?

 

Thank you for your response;

 

John Duff

 

You actually answered my question, without realizing it. If a mirror is stationary and light hits it, and imparts momentum the mirror begins to move. The reflected light is then doppler shifted (red shifted, because the mirror begins to move away). If you calculate the doppler shift, and compare it to the energy gained by the mirror, you'll find that they balance out. That is, the slight red shift in the light does indeed create the extra energy that the mirror gets. However, if you hold the mirror stationary the whole time, then the light need not impart any energy to the system, as the mirror is not moving and has not heated, so no transfer of energy has taken place.

-Will

[johnduff]

I`m havinhg big troubles trying to post replies

This is a fool-around message to see if I can figure out what I`m doing wrong

john duff

[Tormod]

I`m havinhg big troubles trying to post replies

This is a fool-around message to see if I can figure out what I`m doing wrong

john duff

 

Please use our test forum for testing!

[Qfwfq]

But consider the case where the mirrors velocity is zero. Light applies a force to the mirror, causing the mirror to move, gain momentum, and kinetic energy. My question is, "Where does the energy come from?"

Of course, if the mirror's velocity remained zero the work done would be zero. If it acqires a tiny velocity during the collision, the work is tiny. As you're talking about an impulsive interaction, it makes sense to consider the velocity value half-way between that before and that after the collision.

 

Actually, this supposes the mirror being perfectly rigid but, it would be more realistic to consider the surface interacting with the photon, which in turn pushes the deeper atoms and so on, causing a slight energy dispersion. Considering this, there would be a slight redshift even when the mirror is held still. Very very slight, I'd say, but still no mirror would be quite perfect.