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A telescope is advertised as providing a magnification of magnitude 41 using an eyepiece of focal length \(4.0 \cdot 10^{1} \mathrm{~mm}\). What is the focal length of the objective?

Short Answer

Expert verified
Answer: The focal length of the objective lens is 1640 mm.

Step by step solution

01

Recall the magnification formula for a telescope.

The magnification (M) of a telescope can be calculated using the formula: 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.
02

Substitute the given values into the formula.

We are given: M = 41 f_e = 4.0 * 10^1 mm Now, we can substitute these values into the magnification formula: 41 = (f_o) / (4.0 * 10^1 mm)
03

Solve for the focal length of the objective lens (f_o).

To solve for f_o, we can multiply both sides of the equation by f_e, which is 4.0 * 10^1 mm: 41 * (4.0 * 10^1 mm) = f_o
04

Calculate the focal length of the objective lens.

Now, we can perform the calculation: f_o = 41 * (4.0 * 10^1 mm) = 41 * 40 mm = 1640 mm
05

State the answer.

The focal length of the objective lens is 1640 mm.

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