# I Recoil on mirrors and conservation of momentum

1. Mar 28, 2016

### 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 alot of energy to use for useful effect.

Last edited: Mar 28, 2016
2. Mar 28, 2016

### ZapperZ

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

Zz.

3. Mar 28, 2016

### Staff: Mentor

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

4. Mar 28, 2016

### A.T.

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

5. Mar 28, 2016

### Danyon

Oh okay

6. Mar 28, 2016

### Danyon

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?

7. Mar 28, 2016

### ZapperZ

Staff Emeritus
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.

8. Mar 28, 2016

### Danyon

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?

9. Mar 28, 2016

### A.T.

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

10. Mar 28, 2016

### ZapperZ

Staff Emeritus
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.

11. Mar 28, 2016

### Danyon

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

12. Mar 28, 2016

### Staff: Mentor

Your reasoning is backwards. The amount of momentum transfered 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.

13. Mar 28, 2016

### Danyon

Okay, thanks. I just got a bit mixed up