A Galileo telescope has an objective of focal length `100cm` and magnifying power 50. The distance between the two lenses in normal adjustment will be

Options

A. 150 cm
B. 100 cm
C. 98 cm
D. 200 cm

Explanation

To solve the problem, we need to find the distance between the two lenses of a Galileo telescope in normal adjustment. We are given the focal length of the objective lens (F₀) and the magnifying power (M).

### Step-by-Step Solution:

1. **Identify the given values:**
- Focal length of the objective lens (F₀) = 100 cm
- Magnifying power (M) = 50

2. **Use the formula for magnifying power:**
The magnifying power (M) of a telescope is given by the formula:
\[ M = \frac{F₀}{Fₑ} \]
where Fₑ is the focal length of the eyepiece.

3. **Rearrange the formula to find Fₑ:**
From the magnifying power formula, we can express Fₑ as:
\[ Fₑ = \frac{F₀}{M} \]

4. **Substitute the known values:**
Now, substituting the values of F₀ and M into the equation:
\[ Fₑ = \frac{100 \text{ cm}}{50} = 2 \text{ cm} \]

5. **Calculate the distance between the two lenses (L):**
The distance between the two lenses in a Galileo telescope is given by:
\[ L = F₀ - Fₑ \]
Now substituting the values of F₀ and Fₑ:
\[ L = 100 \text{ cm} - 2 \text{ cm} = 98 \text{ cm} \]

6. **Final answer:**
The distance between the two lenses in normal adjustment is **98 cm**.