You are not logged in. [Login] Entrance · Main Index · Search · New user · Who's Online FAQ · Calendar

Equipment Discussions >> ATM, Optics and DIY Forum

Pages: 1
Bob Myler
Carpal Tunnel

Reged: 05/18/06

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

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?

 Post Extras:
GlennLeDrew
Postmaster

Reged: 06/18/08

Re: How Smooth is a One Mile-Wide Mirror? [Re: Bob Myler]
#5628589 - 01/17/13 06:09 PM

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.)

 Post Extras:
Bob Myler
Carpal Tunnel

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

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?

 Post Extras:
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

Your math is correct. Interesting way of looking at it.

 Post Extras:
Bob Myler
Carpal Tunnel

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

Thank you. Using the very large to explain the very small - seems to help some better visualized the very small...

 Post Extras:
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

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

 Post Extras:
dpwoos
Pooh-Bah

Reged: 10/18/06

Loc: United States
Re: How Smooth is a One Mile-Wide Mirror? [Re: Jon Isaacs]
#5629139 - 01/17/13 11:41 PM

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.

 Post Extras:
Pages: 1

Extra information
7 registered and 17 anonymous users are browsing this forum.

Moderator:  ausastronomer, richard7, Starman81

Forum Permissions
You cannot start new topics