The focal length of objective & eyepiece of an telescope are 50 cm & 5 cm respectively.If the telescope is focussed for distinct vision on a scale distant 2 m from its objective, then its magnifying power will be

To find the magnifying power of a telescope, we can use a straightforward formula that relates the focal lengths of the objective and the eyepiece, as well as the distance of the object being viewed. In this case, we have the focal lengths of the objective and eyepiece, and we know the distance to the object. Let's break it down step by step.

Understanding the Components

The telescope consists of two main lenses: the objective lens and the eyepiece lens. The focal lengths are given as follows:

• Focal length of the objective (F_o): 50 cm
• Focal length of the eyepiece (F_e): 5 cm

Distance to the Object

The object is located at a distance of 2 meters (200 cm) from the objective lens. This distance is crucial for calculating the magnifying power.

Calculating the Magnifying Power

The formula for the magnifying power (M) of a telescope is given by:

M = (F_o / F_e)

However, when the telescope is focused on a distant object, we also need to consider the distance of the object. The formula can be adjusted to:

M = (F_o / F_e) + 1

In this case, since the object is at a distance much greater than the focal lengths involved, we can simplify our calculations using just the focal lengths.

Plugging in the Values

Now, substituting the values into the formula:

• F_o = 50 cm
• F_e = 5 cm

Calculating the magnifying power:

M = (50 cm / 5 cm) = 10

Final Result

The magnifying power of the telescope, when focused for distinct vision on an object 2 meters away, is 10. This means that the telescope makes the object appear 10 times larger than it would to the naked eye.

Practical Implications

This magnification is particularly useful in astronomy and other fields where observing distant objects in detail is essential. A higher magnifying power allows for better observation of celestial bodies, but it can also lead to a narrower field of view and may require more precise alignment of the telescope.