Question

A refracting telescope has the objective lens of focal length \(10.0 \mathrm{~m} .\) Assume it is used with an eyepiece of focal length \(2.00 \mathrm{~cm} .\) What is the magnification of this telescope?

Short answer

Answer: The magnification of the refracting telescope is 500.

Step-by-step solution

Write down the given parameters and magnification formula.

We are given the objective lens focal length of \(10.0\mathrm{~m}\) and the eyepiece focal length of \(2.00\mathrm{~cm}\). Let \(f_o\) represent the focal length of the objective lens, and \(f_e\) represent the focal length of the eyepiece lens. The formula for the magnification, \(M\), of a telescope is given by: $$ M = \frac{f_o}{f_e} $$

Convert focal lengths to the same units.

In order to calculate the magnification using the given formula, we must ensure that both focal lengths are in the same units. In this case, since the eyepiece focal length is given in centimeters, we can either convert it to meters or convert the objective lens focal length to centimeters. We'll choose to convert the eyepiece focal length to meters. To convert from centimeters to meters, we simply multiply by 0.01: $$ 2.00\,\text{cm} \times 0.01 = 0.02\,\text{m} $$ Now, the eyepiece focal length becomes \(0.02\mathrm{~m}\).

Apply the magnification formula.

Plug the given focal lengths into the magnification formula: $$ M = \frac{f_o}{f_e} = \frac{10.0\,\text{m}}{0.02\,\text{m}} $$

Calculate the magnification.

Divide the objective lens focal length by the eyepiece focal length to find the magnification: $$ M = \frac{10.0\,\text{m}}{0.02\,\text{m}} = 500 $$ The magnification of the refracting telescope is 500.