A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm is used, what is the angular magnification of the telescope?

To determine the angular magnification of a telescope, we can use a straightforward formula that relates the focal lengths of the objective lens and the eyepiece. The angular magnification (M) is given by the ratio of the focal length of the objective lens (F_o) to the focal length of the eyepiece (F_e). The formula is expressed as:

Angular Magnification Formula

The formula for angular magnification is:

M = F_o / F_e

Given Values

• Focal length of the objective lens (F_o) = 15 m
• Focal length of the eyepiece (F_e) = 1.0 cm = 0.01 m

Calculating Angular Magnification

Now, substituting the values into the formula:

M = 15 m / 0.01 m

Calculating this gives:

M = 1500

Understanding the Result

This means that the telescope magnifies the image by a factor of 1500 times. In practical terms, if you were looking at a distant object, it would appear 1500 times larger than it would to the naked eye. This level of magnification is particularly useful in astronomical observations, allowing astronomers to see distant celestial bodies in much greater detail.

Real-World Application

For example, if you were observing a star that is normally just a point of light, with this telescope, you could see it as a much larger and more detailed object. This capability is essential for studying the structure of stars, planets, and other astronomical phenomena.

In summary, the angular magnification of the telescope with the given focal lengths is 1500, enabling impressive views of the universe beyond our immediate surroundings.