Question

A telescope, consisting of two lenses, has an objective lens with focal length \(646.7 \mathrm{~cm}\) and an eyepiece with focal length \(5.41 \mathrm{~cm} .\) What is the absolute value of its angular magnification?

Short answer

Answer: The approximate absolute value of the angular magnification is \(119.5\).

Step-by-step solution

Write down the given data

We are given the following data: Focal length of the objective lens (F_O): \(646.7\mathrm{~cm}\) Focal length of the eyepiece (F_E): \(5.41\mathrm{~cm}\) Now, we need to find the absolute value of the angular magnification (M) of the telescope using the formula.

Apply the formula for angular magnification

The formula for angular magnification is given by: \( M = \frac{F_O}{F_E} \) Now, we plug the given values into the formula: \( M = \frac{646.7\mathrm{~cm}}{5.41\mathrm{~cm}} \)

Calculate the magnification

Divide the focal length of the objective lens by the focal length of the eyepiece: \( M \approx 119.5 \) Since we only need the absolute value, the angular magnification of the telescope is \(| M | = 119.5\). Therefore, the absolute value of the angular magnification of the telescope is approximately \(119.5\).