# Minimum angle required for resolution

1. Apr 5, 2009

### msk172

1. The problem statement, all variables and given/known data

The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of 295 m diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency of 200 MHz, what is the angle between two stars that can barely be resolved?

2. Relevant equations

θmin= (1.22λ)/D

θmin= minimum angle required for resolution (rad)
λ = wavelength
D = diameter of aperture

3. The attempt at a solution

Should be fairly straightforward but I'm getting hung up on what I am sure is something silly. The equation above should be all that is needed. Just do (1.22*1.5)/295 as specified by the problem for θmin (in radians). I know I must be overlooking something simple, so any help is greatly appreciated. Thanks!

2. Apr 5, 2009

### Redbelly98

Staff Emeritus
Don't worry, this one really is that simple

3. Apr 5, 2009

### msk172

Heh. Figured as much. I'll keep looking at it, and I'm sure it will come to me eventually. Thanks.

Last edited: Apr 5, 2009
4. Apr 5, 2009

### Redbelly98

Staff Emeritus
What do you mean "it will come to me eventually"?

(1.22*1.5)/295​

You are just a few calculator keystrokes from having the answer. (In radians)

5. Apr 5, 2009

### msk172

Well, 1.22 times the wavelength (1.5m) divided by D (295m) should equal θmin in radians, no? That is how I'm interpreting it, at least.

6. Apr 5, 2009

### Redbelly98

Staff Emeritus
Yes, exactly.

7. Apr 5, 2009

### msk172

That's what I thought. System says that's incorrect, though.

8. Apr 5, 2009

### Redbelly98

Staff Emeritus
Weird. All I can think is it's either a significant figures or units problem. But with radians, expressing no units should be acceptable. I guess you have rechecked the calculation.

Can't think of anything else, but if I do I'll post here again.