Diffraction Equation HELP

Five_Swords

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11 years ago

I have been pondering for a while now and I was wondering if anyone here could help me (step-by-step) how the answer was derived from the picture shown. I need to truly understand the equation so if you could really dumb it down I would be very appreciative

Thank you

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bio_man

wrote...

Educator

11 years ago

Lambda is the wavelength of light. D is the numerical aperture of the focusing lens.

Hope this gives some insight.

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Five_Swords Author

wrote...

11 years ago

Thank you for taking the time to look over my question.
I was wondering if you could show me (step-by-step) how my professor derived 15.000 meters as the answer using that triangle. I have plugged in countless numbers, used sin, cos, tan and I cannot even get remotely close to 15.000 meters. I have an exam this week and although this exact question obviously won't be on the test, the professor mentioned that he will use it with different numbers. So I just need to know how to get the answer from start to finish and then I can take it from there myself.

Thanks once again

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bio_man

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Educator

11 years ago

See the attachment...

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mikael

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Five_Swords Author

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11 years ago

Bio_Man

I just wanted to say thank you for being so detailed in your response and for using different colors so that I could easily follow your train of thought. It's all crystal clear at this point! The test is taking place in a couple of days and I feel very comfortable to leave the diffraction portion of it aside for now and focus on the remainder of the chapters. Once again, I truly appreciate your help!

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bio_man

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Educator

11 years ago

My pleasure...

If you need more help, start a new thread.

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Five_Swords Author

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11 years ago

Thanks, I do have one additional question
This question pertains to the previous one.
If the distance of separation between Planet A and Planet B is 2.000.000 km and the distance from Earth is 600.000.000 km, what is the D (Diameter)?

I got the answer:
D= 4.52 x 10(-7) km
(0.000000452 km OR 0.000452 meters)

Would you say that this is accurate or somewhere close to it?

You can use my first attachment if you feel like you need it (Which I doubt)

Post Merge: 11 years ago

I also got θ to be 1.48 during the course of the calculation. Right/ Wrong?

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bio_man

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Educator

11 years ago

Hmm... I'm not following here. I used the formula: Theta = 2 / d. Does little d stand for diameter?

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Five_Swords Author

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11 years ago Edited: 11 years ago, Five_Swords

We got vastly different answers. Maybe I did something wrong. Ill use your notes to cross reference my work. Once again, I appreciate your help

d = Distance
D= Diameter

Post Merge: 11 years ago

This is what I got:

θ=2.000.000/600.000.000
θ=0.00333

0.00333=1.22(0,00000055/D) (0.00000055=Wavelength (constant)

0.00000055/0.00333 = 0.000165165

0.000165165=1.22D

0.000165165/1.22=D

0.000135281=D

Answer: D (Diameter) is 0.000135281 km OR 1.35281x10(-4) km

Does this sound like a plausible answer?

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bio_man

wrote...

Educator

11 years ago

Hi again, Five_Swords

What ended up being the correct answer?

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