Microwave Emitting Star, and detector with diffraction

1. Dec 12, 2008

TFM

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

A microwave detector is located 0.5m above the surface of a large lake far from the shore. As a star, emitting monochromatic microwave radiation of 21cm wavelength, rises slowly above the horizon, the detector indicates successive maxima and minima in the signal intensity. At what angle above the horizon is the star when the first maximum is received?

2. Relevant equations

Not sure of relevance:

Youngs:

$$I(s) = I_0 cos^2 \frac{kDs}{2}$$

Infinite Grating:

$$I(s) = I_0 \sum^\{infty}_{n = -\infty}\sigma (s-\frac{n\lambda}{d})$$

3. The attempt at a solution

I am slightly unsure about this question. My main problem is that I am unsure where the diffraction is coming from? Any help would be most appreciated.

Included is a diagram of my interpretation of the situation

TFM

Attached Files:

• Star and Microwave detector.jpg
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2. Dec 12, 2008

turin

I can't see your image file yet, but I'll bet that there is no diffraction, but that there is reflection. What physics principle allows for the variation in intensity?

3. Dec 12, 2008

TFM

I wouldn't worry to much about the diagram, its one I did myself, and not my best.

I didn't think it would be diffraction, but is the only thing I could think of that gives maxima and minima.

I am probably missing out on something simple, but I can't think exactly what else would give maxima and minima (regularly any way - I do Astrophyics as well, so Dust clouds spring to mind otherwise, but that's not relevant with this question)

TFM

4. Dec 12, 2008

turin

Diffraction does not give maxima and minima, but it usually leads to another phenomenon that does. Anyway, like I said, it probably isn't diffraction. You need to read your book to find out what physical phenomenon I'm talking about. Consider two waves, and what happens when they try to occupy the same space.

5. Dec 12, 2008

TFM

Ah Interference - I feel so silly for not thinking of it sooner.

Would that not need two sources though?

TFM

6. Dec 12, 2008

turin

EXCELLENT question! Hint: method of images. Oh, yeah, don't neglect phase changing behavior at material interface.

7. Dec 12, 2008

TFM

I don't think I have studied Method of Images?

This seems like an optics question - trouble is, I didn't do Optics (1st Year Astrophysics didn't do that course, only Theoretical, and non-Astro) - This question is from a 'Skills' Course.

TFM

8. Dec 14, 2008

TFM

Looked up Method of Images, and it seems to be about electric charges???

TFM

9. Dec 15, 2008

TFM

TFM

10. Dec 15, 2008

Carid

It's so romantic to see the moon reflected in the surface of a lake. Pity it doesn't emit much in the way of microwaves.

11. Dec 15, 2008

TFM

It is indeed.

But wouldn't the reflected waves be going upwards, and, although they would interfere with the incoming waves, they wouldn't reach the detector interfered - the incoming waves are only interfered whilst the other waves are there?

TFM

12. Dec 15, 2008

Carid

In a harbour you'll see a wave bouncing off the quay and interfering with any other wave that happens to be about. The microwaves beaming down from the star behave in much the same way.
We'll get our first maximum when the path lengths differ by a single half wavelength; only half because of the phase inversion at the water surface.
I reckon the star will be 6 degrees above the horizon.

13. Dec 15, 2008

TFM

Okay. So what sort of equations might be useful? This is supposed to be a big question, so I am assuming there is quite a few bits of work involved in getting out the right answer?

TFM

14. Dec 15, 2008

Carid

Draw one ray from your star to the detector.
Draw another arriving at the detector after being reflected at the lake surface.
Do a bit of trigonometry.
Find angle.

15. Dec 15, 2008

TFM

Okay so (when it is accepted), is this the right sort of diagram?

TFM

Attached Files:

• Star and Microwave detector 2.jpg
File size:
6.3 KB
Views:
93
16. Dec 15, 2008

turin

Sorry for leaving you high and dry, but I see that Carid adopted my post. Also, sorry about that "method of images hint"; I had thought you might have been able to find it more broadly applicable than static, charged monopoles. I'll try to give it a different way. Have you studied flat mirrors, yet?

17. Dec 16, 2008

TFM

That's okay

I didn't do optuics, so no, I don't believed I have studied much on flt mirrors. I nknow snells law, and that the anlge of incidenc = angle of reflection, although that isn't shown well on the diagram.

TFM

18. Dec 16, 2008

turin

We're in more trouble than I thought. Do you have a freshman physics book with a chapter on mirrors and a chapter on wave phenomena?

19. Dec 17, 2008

TFM

I Know, I can't spell flat!

We have a result. I have a textbook, University Physics, and it has FOUR chapters dedicated to optics

Including one on interference and one chapter section on reflection (and refraction) on a plane surface, and on a sphereical surface.

Having a look...

Law of reflection:

$$\theta_a = \theta_b$$

where these are the angles that the light hits and is reflected (assuming non perpendicular) - this is what a stated in a previous post.

Also, destructive interference:

$$r_2 - r_1 = (m + \frac{1}{2})\lambda , (m = \pm1, \pm2, \pm3...)$$

Are these useful? I think they maybe...

TFM

20. Dec 18, 2008

Carid

TFM,

I'm fairly new in these parts and it seems I have transgressed the unwritten law in barging into a thread where someone else was already trying to help. Is that the way it works?

By the way, did you find anything incorrect or misleading in the contributions I made?