Two stars are 4.4 x 10^11 m apart and are equally distant from the earth.?

Question

Two stars are 4.4 x 10^11 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.28 m and just detects these stars as separate objects. Assume that light of wavelength 540 nm is being observed. Also, assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.

anakin_louix · Accepted Answer

Ok, here you need to use the Rayleigh's diffraction :

For example : the Rayleigh's diffraction says :

wavelenght / diameter = theta

theta, angle form by the rays of light coming from the stars

diameter = diamter of the lens:

540*10^-9 / 1.28 = theta

And, for example, you will find a circular sector :

L = theta*distance

4.4*10^11 = 540*10^-9 /1.28*distance

distance = 0.01*10^20 = 10^18 meters

Look, review that part of your theory, because, the best way to solve this problem, is making a graphic of it, but always remember :

wavelenght / diameter = theta

Hope that helps

huyna · Answer

Equally Distant

Anonymous · Answer

The pink great could be great and funky. the biggest sequence could be warm and shiny, like the solar. The blue great could be youthful, particularly warm and extremely shiny. The pink dwarf could be cool and uninteresting. Which leaves the white dwarf. nonetheless boiling warm from the celebrities dying which created it, yet dim because it no-longer has nuclear fusion to maintain it going. The white dwarf. desire this facilitates.

Codi · Answer

θmin ~ 1.22 λ/D   --> D = diameter of lens
θmin is in radians so plug it in for "r" down below

Then.. 
θ = s/r    --> s = distance btw stars 
θ = max dis. stars could be from Earth = answer

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Two stars are 4.4 x 10^11 m apart and are equally distant from the earth.?

4 Answers