The angular magnification of a refracting telescope is 40 x.When the object and final image are both at infinity,the distance between the eyepiece and the objective is 143.5 cm.The telescope is used to view a distant radio tower.The real image of the tower,formed by the objective,is 6.0 mm in height.The focal point of the eyepiece is positioned at the real image.What is the focal length of the objective lens?
A) 137 cm
B) 138 cm
C) 139 cm
D) 140 cm
E) 141 cm

Question

Quizplus · Accepted Answer

Using the formula for angular magnification of a refracting telescope:
Magnification = -fo/fe
where fo is the focal length of the objective lens and fe is the focal length of the eyepiece.
Substituting the values given:
40 = -fo/fe
Since the focal point of the eyepiece is positioned at the real image formed by the objective, we can use the thin lens equation for the objective lens:
1/f = 1/do + 1/di
where f is the focal length of the objective lens, do is the object distance (which is infinity in this case) and di is the image distance (which is also infinity in this case since the final image is at infinity). Rearranging the equation, we get:
f = do * di / (do + di)
Since both do and di are infinity, f is undefined. However, we can use the fact that the distance between the objective and eyepiece is 143.5 cm to find the ratio of fo to fe:
fo + fe = 143.5
fe = -fo/40
Substituting this expression for fe in the previous equation:
fo - fo/40 = 143.5
39fo/40 = 143.5
fo = 140 cm, rounded to the nearest integer. Therefore, the answer is D.

The Angular Magnification of a Refracting Telescope Is 40 X