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Saturday, May 14, 2011

PM's Question Time

I thought I'd take a moment again to answer some of your questions...

Carrie asked about this post, "Having never heard of a Fresnel prism before, I was hoping you would write (and post a photo) about it!"
I'm not too clear on how the prism bit fits in, but I know they're related to Fresnel lenses.  Normally, for a certain magnification, you need a certain thickness of lens.  For large magnifications, the thickness can become prohibitively large, so Augustin-Jean Fresnel developed a method to get the large magnification without the large lens.  Rather than shaping the lens as a single curved surface, you divide the lens into zones.  Each zone has the same overall curvature, but they are discontinuous, allowing a large amount of material to be left out.  Here's a schematic (from Wikipedia):
The two lenses have the same magnification, but the Fresnel lens (1) is significantly thinner than the traditional lens (2).  My guess is that the same principle can be applied to prisms – a single prism would need to be excessively thick to accomplish the correct shift distance, so instead it's divided into many smaller prisms.

Chris asked about this post, "Speaking of quantum mechanics, what about laser speckle? When a coherent beam of light scatters off of a rough surface, you get an interference pattern whose intensity varies randomly in the quantum mechanical sense. Theoretically you could inspect tiny areas and get random numbers. Maybe hard in practice.  Can nonlinear phenomena at macroscopic scales give you random numbers?"
Neat idea, Chris, I think laser speckle could work just fine.  When I used to do quantum dot research, the lab was often filled with scattered light from the green laser we used.  When it hit the walls, it had a very clear speckling.  As it happens, I still have a picture.
As for your second question, I'm not sure why not.  Did you have a possible counter-example in mind?

Nate commented on this post, "I think that assuming that the car body is perfectly rigid is a big factor in the low speed you're seeing. The first few things to hit the ground should crumple and increase drag."
I'm not sure whether that would make much difference actually.  Normally, friction doesn't depend on the surface area in contact.  It's quite possible that the normal model for friction doesn't work well in this case though, since the axle could dig into the pavement (acting even more like a pole vaulter).  Even if the real minimum speed is as much as 60 mph though, it's still a speed that people drive at.

Thanks once again for the questions/comments.  I'm thinking this sort of thing will have to be a regular feature...

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