Help please

[Brodie3857]

A The Keck telescope on Mauna Kea has an angular resolution on Earth of half an arcsecond.

How far away (in meters) could you read ("resolve the letters of") a book with 3 mm square type, using the Keck telescope on Earth?

B  In space, the angular resolution of the Keck telescope is govererned by the diffraction limit.

How far away could you read the same book, using the Keck telescope in space? Please express your answers in units of meters.

 

answers please 

[vlaiv]

It would be helpful if you would expand on your question - why do you want it answered, what sort of explanation are you hoping for, etc ...

As it is now, it just looks like homework assignment that you need help with, and that is also fine, but it would be much better if you did say that you need help with that sort of thing.

From your post, one could possibly conclude that it's a "pop quiz" for members, or something like that, and I'm not sure how many will be willing to participate. On the other hand, I'm almost certain that people will be willing to help if you explain it and ask nicely.

[Steve]

7 minutes ago, vlaiv said:

It would be helpful if you would expand on your question - why do you want it answered, what sort of explanation are you hoping for, etc ...

As it is now, it just looks like homework assignment that you need help with, and that is also fine, but it would be much better if you did say that you need help with that sort of thing.

What he said ^ 🙂 

[upahill]

The exact phrasing of the question has been asked before. On here and googles Think its part of an online astronomy course?

 

 

[Cornelius Varley]

The answer to your questions is 42. The point of my reply is that you don't learn anything if you simply ask someone else for the answer.

[JRWASTRO]

Greetings Brodie,

Re: B  " In space, the angular resolution of the Keck telescope is govererned by the diffraction limit. "

Really ? Where did you read this ?

About diffraction limited optics, These books have definitions of what it means when an optic is diffraction limited:

1.  Introduction to Fourier Optics

by Joseph W. Goodman

See p. 129 " An imaging system is said to be diffraction limited if ..... "

2. Aberration Theory Made Simple. (SPIE PRESS Tutorial Text)

by Virendra N. Mahajan

See p. 79  " The aberration-free image of an object is also called its diffraction-limited image .... "

3. Basic Optics for the Astronomical Sciences (SPIE PRESS)

James B. Breckinridge

P. 227 10.2.2 High-angular-resolution astronomy: stelar diameters.

BTW : Nice picture of the Keck Telescopes on the front cover.

4. Diffraction, Fourier Optics and Imaging

Oran K. Ersoy

p.142  " An optical system is diffraction limited if  ... "

Ersoy, here, refers to Goodman (ref # 1 above).

I have other books but the above references will help you answer your question.

Jeremy

[robin_astro]

It is a dumb question anyway.  Using the figure of 0.5 arcsec (presumably as measured from earth using an object outside the atmosphere), the distance to the hypothetical book held in front of the telescope in part A is (spoiler alert) much less than the depth of the atmosphere, even from Mauna Kea so we would need to know the resolution as a function of atmospheric thickness. 

I sometimes wonder if brighter students who actually think, fail at the first hurdle because of this sort of "spherical cow" type question. Here is another one

 

[ollypenrice]

I think the OP should apply for time on the Keck in order to derive a thoroughly empirical answer.

 

[Ags]

But what font is used for the 3mm text?

[vlaiv]

3 hours ago, Ags said:

But what font is used for the 3mm text?

About 35.433070866141732283464566929134 points in size on 300dpi printer