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An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance

1. 37.3 cm
2. 46.0 cm
3. 50.0 cm
4. 54.0 cm

Correct answer: 46.0 cm

Solution

The separation between the lenses in an astronomical telescope is given by the sum of the focal lengths of the objective and eyepiece when the telescope is in normal adjustment. However, since the object is not at infinity, the lens separation is adjusted using the lens formula for the objective: 1/f = 1/v - 1/u. Solving for v (image distance for the objective) and adding the eyepiece focal length gives the separation as 46.0 cm.

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