Recoil on mirrors and conservation of momentum

[Danyon]

I wanted to know whether or not a perfect mirror would experience recoil when light reflects off it, and I also wanted to know whether or not light can cause a recoil during total internal reflection. I suspect that the recoil is negligible (Even with a normal mirror) and that you could easily make a reaction-less drive for a spacecraft by simply firing a high powered laser at a mirror at the back of the spacecraft so that the light reflects back and hits the front. The laser will recoil, pushing the craft forward and the reflected light will also push it forward. This seems to violate conservation of momentum. Though it would take a lot of energy to use for useful effect.

 

[ZapperZ]

There can be such recoil. This is the basis for the presence of radiation pressure and the concept behind solar sails.

Zz.

 

[Dale]

you could easily make a reaction-less drive

No. You could certainly use light as your exhaust, but in the end that is a radiation reaction and not reaction less.

 

[A.T.]

The laser will recoil, pushing the craft forward and the reflected light will also push it forward.

The mirror will push it back. Drop the mirror and just point a laser backwards.

 

[Danyon]

No. You could certainly use light as your exhaust, but in the end that is a radiation reaction and not reaction less.

Oh okay

 

[Danyon]

The mirror will push it back. Drop the mirror and just point a laser backwards.

If the mirror pushes back with force equal to the force of the photons at the front of the ship that would imply that half of the energy/momentum of the photon was imparted on the mirror. I don't think the mirror will push back equally. When I look into a mirror I see that the colour of the objects I see doesn't change from the objects original colour. This tells me the energy of the photons does not change significantly after reflection, only a small portion of the energy and momentum of the photon will go into recoiling the mirror while the majority of the energy and momentum will act on the front of the ship when the light is absorbed...Is my reasoning flawed?

 

[ZapperZ]

Er... do you know how to do impulse calculation when an object, say, a tennis ball, bounces off a wall? This is no different!

Zz.

 

[Danyon]

Er... do you know how to do impulse calculation when an object, say, a tennis ball, bounces off a wall? This is no different!

Zz.

I don't know how, though the energy of the photon is mostly conserved after reflection, the more energy you have the more momentum you have. the mirror has less momentum transferred to it than the front of the ship does...At least it looks that way to me. where am I going wrong?

 

[A.T.]

Is my reasoning flawed?

To make any sense you should try to keep energy and momentum apart.

 

[ZapperZ]

I don't know how, though the energy of the photon is mostly conserved after reflection, the more energy you have the more momentum you have. the mirror has less momentum transferred to it than the front of the ship does...At least it looks that way to me. where am I going wrong?

Where you are going wrong is trying to tackle this before you understand basic mechanics.

And you really should, as has been stated, separate out "energy" and "momentum". Your question deals with the CHANGE in momentum of an object that is hitting a surface, because the rate of change of momentum of the object signifies the force it exerted onto the surface. For an object that hits and bounces of a surface elastically, the change in momentum is 2p, where p is the initial momentum coming in. The rate of change of this momentum is the force acting on the surface.

Zz.

 

[Danyon]

Where you are going wrong is trying to tackle this before you understand basic mechanics.

And you really should, as has been stated, separate out "energy" and "momentum". Your question deals with the CHANGE in momentum of an object that is hitting a surface, because the rate of change of momentum of the object signifies the force it exerted onto the surface. For an object that hits and bounces of a surface elastically, the change in momentum is 2p, where p is the initial momentum coming in. The rate of change of this momentum is the force acting on the surface.

Zz.

Okay, I'm a little rusty I haven't done this in a little while. I'l think it over again

 

[Dale]

I don't know how, though the energy of the photon is mostly conserved after reflection, the more energy you have the more momentum you have. the mirror has less momentum transferred to it than the front of the ship does...At least it looks that way to me. where am I going wrong?

Your reasoning is backwards. The amount of momentum transferred to the mirror is double the amount transferred to the front. Think of someone throwing a ball back and bouncing it off a wall. The ball starts with momentum 0. The ball is thrown with momentum -p. It bounces so the momentum becomes p. Then it is caught so it's momentum becomes 0.

The energy transfer is not comparable so ignore it for now. The reflection is an elastic collision and the absorption is plastic.

 

[Danyon]

Your reasoning is backwards. The amount of momentum transferred to the mirror is double the amount transferred to the front. Think of someone throwing a ball back and bouncing it off a wall. The ball starts with momentum 0. The ball is thrown with momentum -p. It bounces so the momentum becomes p. Then it is caught so it's momentum becomes 0.

The energy transfer is not comparable so ignore it for now. The reflection is an elastic collision and the absorption is plastic.

Okay, thanks. I just got a bit mixed up