Question
Problem 19.33
Two light bulbs are 1.5 m apart.
From what distance can these light bulbs be marginally resolved by a small telescope with a 4.0 cm-diameter objective lens? Assume that the lens is limited only by diffraction and lambda = 600 nm.
Two light bulbs are 1.5 m apart.
From what distance can these light bulbs be marginally resolved by a small telescope with a 4.0 cm-diameter objective lens? Assume that the lens is limited only by diffraction and lambda = 600 nm.
Answers
The angular resolution limit for two point sources of equal intensity is
d(theta) = 1.22(lambda)/D,
in radians, where D is the aperture diameter. This assume good atmospheric vewing conditions ("seeing").
If the viewing distance is X (meters),
1.5/X = 1.22*(600*10^-9 m)/(0.04 m)
Solve for X, in meters
X = 1.5*0.04/[1.22*600*10^-9)]
Solve for X
d(theta) = 1.22(lambda)/D,
in radians, where D is the aperture diameter. This assume good atmospheric vewing conditions ("seeing").
If the viewing distance is X (meters),
1.5/X = 1.22*(600*10^-9 m)/(0.04 m)
Solve for X, in meters
X = 1.5*0.04/[1.22*600*10^-9)]
Solve for X
8=======3