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Bob Myler
scholastic sledgehammer

Reged: 05/18/06

Loc: St Louis, MO
How Smooth is a One Mile-Wide Mirror?
#5628485 - 01/17/13 05:11 PM
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Would someone please check my math?

We start with an 8" astronomical mirror - figured to within 1/8th wave surface accuracy:

A. Wavelength of green light: 550NM (0.00000055 Meters)
B. Convert this to inches (x's 39.37): 0.00002165"
C. 1/8th of the above would be 0.0000027"

So - just how smoooooth is 2.7 millionths of an Inch?

If we were to expand the diameter of our 8" mirror to One Mile - its (6 to 1 ratio) edge would stand almost 300 yards tall - and its finished face would have a surface accuracy of approximately 1/50th of an inch.

Folks, is that a reasonable approximation of reality?

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GlennLeDrew
Postmaster

Reged: 06/18/08

Loc: Ottawa, Ontario, Canada
Re: How Smooth is a One Mile-Wide Mirror? [Re: Bob Myler]
#5628589 - 01/17/13 06:09 PM
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No matter how large the mirror, the surface accuracy must still be to within the same fraction of a wavelength of the part of the electromagnetic spectrum observed. A 3", 300", or 30,000" mirror for visual spectrum work would all need to be figured to the same 1/4 wavefront error.

The allowable error does not scale up with the aperture. If it did, big mirrors would be easier to figure than small ones (discounting the handling issues.)

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Bob Myler
scholastic sledgehammer

Reged: 05/18/06

Loc: St Louis, MO
Re: How Smooth is a One Mile-Wide Mirror? [Re: GlennLeDrew]
#5628620 - 01/17/13 06:26 PM
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Understood.

I'm simply asking: Is a fiftieth of an inch surface error (for a mirror with a diameter of 63,360 inches) - the scaled-up equivalent for another - accurate to an eighth of the wavelength of green light, and having an 8 inch diameter?

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George Kiger
member

Reged: 05/19/06

Re: How Smooth is a One Mile-Wide Mirror? [Re: Bob Myler]
#5628675 - 01/17/13 06:59 PM
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Your math is correct. Interesting way of looking at it.

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Bob Myler
scholastic sledgehammer

Reged: 05/18/06

Loc: St Louis, MO
Re: How Smooth is a One Mile-Wide Mirror? [Re: George Kiger]
#5628688 - 01/17/13 07:11 PM
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Thank you. Using the very large to explain the very small - seems to help some better visualized the very small...

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Jon Isaacs
Postmaster

Reged: 06/16/04

Loc: San Diego and Boulevard, CA
Re: How Smooth is a One Mile-Wide Mirror? [Re: Bob Myler]
#5628807 - 01/17/13 08:14 PM
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Quote:

Understood.

I'm simply asking: Is a fiftieth of an inch surface error (for a mirror with a diameter of 63,360 inches) - the scaled-up equivalent for another - accurate to an eighth of the wavelength of green light, and having an 8 inch diameter?

I once saw a similar comparison. As I recall, it went like this:

If the Hale 200 inch at Palomar were scaled up so that it covered the surface of the United states, the bump would be about 4 inches.

Jon

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dpwoos
Pooh-Bah

Reged: 10/18/06

Re: How Smooth is a One Mile-Wide Mirror? [Re: Jon Isaacs]
#5629139 - 01/17/13 11:41 PM
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I always tell folks that if the diameter of the mirror was 1 mile, then it wouldn't deviate from an ideal paraboloid by more than the thickness of a playing card anywhere on its surface.

Similarly, I tell them that to a giant the Earth is smoother than a basketball.

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