An astronomical telescope of magnifying power `7` consists of two thin lenses `40 cm` apart, in normal adjustment. Calculate the focal lengths of the lenses.

Explanation

To solve the problem of finding the focal lengths of the lenses in an astronomical telescope with a magnifying power of 7, we can follow these steps:

### Step 1: Understand the relationship between the focal lengths and magnifying power
The magnifying power (M) of an astronomical telescope in normal adjustment is given by the formula:
\[ M = \frac{F_O}{F_E} \]
where \( F_O \) is the focal length of the objective lens and \( F_E \) is the focal length of the eyepiece lens. Given that the magnifying power is 7, we can write:
\[ M = 7 = \frac{F_O}{F_E} \]
This implies:
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