Resolving Distant Objects question

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The discussion revolves around calculating the maximum wavelength at which two distant light sources can be resolved using a telescope with a 2.0 cm aperture and an angular separation of 3.0 x 10^-5 radians. The relevant equation used is sin(theta) = 1.22 x lambda/D. An initial calculation yielded a wavelength of 0.492 nm, which was later corrected to 492 nm due to unit confusion, as one nanometer equals 1 x 10^-9 meters. The clarification emphasizes the importance of unit conversion in resolving distant objects. The final consensus confirms the correct wavelength for resolution is 492 nm.
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[SOLVED] Resolving Distant Objects question

Consider a telescope with a small circular aperture of diameter 2.0 centimeters.

If two point sources of light are being imaged by this telescope, what is the maximum wavelength (lambda) at which the two can be resolved if their angular separation is 3.0 x 10^-5 radians?



Relevant equation - sin(theta) = 1.22 x lambda/D


I get - Dsin(theta)/1.22 = lambda
0.02 x sin(3.0 x 10^-5)/1.22 = lambda
= 4.92 x 10^-7
therefore lambda = 0.492 nm

It doesn't seem correct. Any help would be very appreciated.
 
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You're correct its just you have the units confused. It will be 492nm not 0.492. Remember a nanometer is 1 billionth of a meter. So one nanometer is 1x10-9 m.
 
yeah i just figured it out and was coming back to post as you replied, thanks anyway though.
 

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