The distance between the two lenses in an astronomical telescope is 157 cm. It has a magnification of -44.0 .(a) Determine the focal length of the eyepiece.
Question
The distance between the two lenses in an astronomical telescope is 157 cm. It has a magnification of -44.0 .
(a) Determine the focal length of the eyepiece.
Solution
The magnification (m) of a telescope is given by the equation m = -f_o/f_e, where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece.
We can rearrange this equation to solve for f_e: f_e = -f_o/m.
We know that the distance between the two lenses (L) is equal to f_o + f_e. We can rearrange this equation to solve for f_o: f_o = L - f_e.
Substituting the second equation into the first gives us: f_e = -(L - f_e)/m.
Solving this equation for f_e gives us: f_e = L/(m+1).
Substituting the given values L = 157 cm and m = -44 into this equation gives us: f_e = 157/(-44+1) = -3.57 cm.
Therefore, the focal length of the eyepiece is -3.57 cm.
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