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Phase difference and finding theta

So I'm stuck on this Isaac physics problem and wondering on how I would go about it.

Question link: https://isaacphysics.org/questions/reflecting_on_the_cosmos

I've already managed to find the path difference in terms of theta and the height, of detector using basic trig, but I have no clue what to do next.

Can anyone help me please on how I would answer this question.

Thanks.
Original post by Yatayyat
So I'm stuck on this Isaac physics problem and wondering on how I would go about it.

Question link: https://isaacphysics.org/questions/reflecting_on_the_cosmos

I've already managed to find the path difference in terms of theta and the height, of detector using basic trig, but I have no clue what to do next.

Can anyone help me please on how I would answer this question.

Thanks.



Equate the path difference to the wavelength of the microwave to find the angle.
Reply 2
Original post by Eimmanuel
Equate the path difference to the wavelength of the microwave to find the angle.


Why do you equate to the full wavelength?

How would you know that the path difference would be the wavelength?

Also here is how I worked out the path difference, but not sure on the how I could solve for theta if I do equate it to one lambda?

EC28423D-0F53-41E4-A3F5-56E2537F04E1.jpg.jpeg
Original post by Yatayyat
Why do you equate to the full wavelength?

How would you know that the path difference would be the wavelength?

Also here is how I worked out the path difference, but not sure on the how I could solve for theta if I do equate it to one lambda?

EC28423D-0F53-41E4-A3F5-56E2537F04E1.jpg.jpeg

I would answer the first 2 questions first. The question "state" that zero order minimum occurs when the source is at the horizon. So the question is asking for 1st order minimum.

Note that there is a phase change of pi for one ray. In order for the two rays to interfere destructively, the two rays need to have a total phase difference of odd integer pi.

Total phase difference = phase difference due path difference + phase change due to reflection = 2*pi + pi

As for solving, you need to expand sin(90 - 2*theta) and then simplify using cos(2*theta) identity.
Reply 4
Original post by Eimmanuel
I would answer the first 2 questions first. The question "state" that zero order minimum occurs when the source is at the horizon. So the question is asking for 1st order minimum.

Note that there is a phase change of pi for one ray. In order for the two rays to interfere destructively, the two rays need to have a total phase difference of odd integer pi.

Total phase difference = phase difference due path difference + phase change due to reflection = 2*pi + pi

As for solving, you need to expand sin(90 - 2*theta) and then simplify using cos(2*theta) identity.


Okay, so I have taken into account that the total phase difference is 3 pi, and also worked out that the path difference ( delta x) is to be 2h*sin (theta) from using the trig identities 'sin (90 - theta) = cos (2*theta)' and then 'cos( 2 * theta) = 1 - 2 sin^2(theta).

I then used the following equation ' delta x = delta phi * lambda/2 pi, by substituting all the values I know.

Although I still got the wrong angle. What did I do wrong?
(edited 5 years ago)
Original post by Yatayyat
Okay, so I have taken into account that the total phase difference is 3 pi, and also worked out that the path difference ( delta x) is to be 2h*sin (theta) from using the trig identities 'sin (90 - theta) = cos (2*theta)' and then 'cos( 2 * theta) = 1 - 2 sin^2(theta).

I then used the following equation ' delta x = delta phi * lambda/2 pi, by substituting all the values I know.

Although I still got the wrong angle. What did I do wrong?

In the previous post, I mention that the phase difference due to path difference is 2*pi, so
2*h*sin(theta) = lambda

PS: learn to check units on lhs and rhs, it can tell you whether you are on the right track.
Reply 6
Original post by Eimmanuel
In the previous post, I mention that the phase difference due to path difference is 2*pi, so
2*h*sin(theta) = lambda

PS: learn to check units on lhs and rhs, it can tell you whether you are on the right track.


Yes, I just realized I made a silly mistake and forgot to minus pi on both the RHS and LHS.It makes alot of sense now.

Cheers mate this was really helpful :smile:

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