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33. Two stars are 3.7 x
1011 m apart and are equally distant from the
earth. A telescope has an objective lens with a diameter of 1.02 m and just
detects these stars as separate objects. Assume that light of wavelength 550
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. |
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When two objects are “just
resolved” their central diffraction maximum of each object lies on the first
diffraction minimum of the other object and this leads to the minimum angle
of resolving for circular apertures is |
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Now since the stars are far
from Earth, we are dealing with small angles so the following approximation
applies |
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So we can find tangent from |
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Solve for distance from Earth,
L. |
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