Minimun lens size (in meters) that will permit just resolving 2 stars

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The minimum lens size required to resolve two stars 1.1 arcseconds apart using light of 510 nm can be calculated using the formula for diffraction. The first minimum occurs when the slit width "a" satisfies the condition a sin(θ) = λ, where θ is the angle in radians. Given that 1.1 arcseconds equals 1.1/3600 degrees, this angle must be converted to radians for accurate calculations. The discussion emphasizes that understanding the relationship between angle, wavelength, and slit width is crucial for determining the necessary lens size.

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What is the minimun lens size (in meters) that will permit just resolving 2 stars 1.1 seconds apart using light of 510 nm?
For a slit of width a, light of wavelength L, the first minimun occurs at an angle t from the center, assume a slit shaped lens! E=E max L* sin(pi a sin(t)/L)/(pi a sin(t) )
Hint: you don't really need all of this. Resolution implies that the maximun of one image falls on the minimun of the other.
I have really no clue on how to this:cry: please help!
 
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cheez said:
I have really no clue on how to this:cry: please help!
The first minimum occurs when a sin (\theta) = \lambda.



In these problems, often the angles are so small that you may replace sin and tan by the angle itself at the condition of working in radians.

Then a \theta \approx \lambda.

They give you lambda and theta. Just convert theta in radians and solve for "a" which will be the slit width "a"
 
how to calculate theta? thanks you so much!
 
cheez said:
how to calculate theta? thanks you so much!
If one is given the distance between the sources of light (perpendicular to the line of sight) and the distance between the sources and the lens, there is a formula in terms of a tangent. But here you are in luck, they give you the value of theta in the problem!
They are 1.1 arcsecond apart (if they said second, they really meant arcsecond). Do you know what an arc second is? It is one degree divided by 3600 (this comes from the fact that one degree is 60 arcminutes and one arcminute is 60 arcsenonds). So your angle is 1.1/3600 degrees. Now convert that in radians, plug that in the equation and you are done.

Patrick
 
thx for your answer!
 

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