Question

Galileo discovered the moons of Jupiter in the fall of \(1609 .\) He used a telescope of his own design that had an objective lens with a focal length of \(f_{\mathrm{g}}=40.0\) inches and an eyepiece lens with a focal length of \(f_{c}=2.00\) inches. Calculate the magnifying power of Galileo's telescope.

Short answer

Answer: The magnifying power of Galileo's telescope is 20.

Step-by-step solution

Write down the formula for magnification of a telescope

The magnification of a telescope is given by the formula: \(m = \frac{f_{g}}{f_{c}}\) where \(m\) is the magnification, \(f_g\) is the focal length of the objective lens, and \(f_c\) is the focal length of the eyepiece lens.

Plug in the given values

We are given the focal lengths of the objective lens (\(f_g = 40.0\) inches) and the eyepiece lens (\(f_c = 2.00\) inches). Now we can plug in these values into the magnification formula: \(m = \frac{40.0 \, \text{inches}}{2.00 \, \text{inches}}\)

Calculate the magnification

Now we can solve for the magnification: \(m = \frac{40.0 \, \text{inches}}{2.00 \, \text{inches}} = 20\) The magnification of Galileo's telescope is 20. This means that the image seen through the telescope is 20 times larger than what is seen with the naked eye.