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 of finding the distance between the two lenses in a Galileo telescope with a given objective focal length and magnifying power, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between magnifying power (M), focal lengths of the objective (f₀), and the eyepiece (fₑ)**:
\[ M = \frac{f₀}{fₑ} \]

2. **Given values**:
- Focal length of the objective, \( f₀ = 100 \, \text{cm} \)
- Magnifying power, \( M = 50 \)

3. **Substitute the known values into the magnifying power formula**:
\[ 50 = \frac{100}{fₑ} \]

4. **Rearranging the equation to find \( fₑ \)**:
\[ fₑ = \frac{100}{50} = 2 \, \text{cm} \]

5. **Now, use the formula for the distance between the two lenses (L)**:
\[ L = f₀ - fₑ \]

6. **Substituting the values of \( f₀ \) and \( fₑ \)**:
\[ L = 100 \, \text{cm} - 2 \, \text{cm} = 98 \, \text{cm} \]

7. **Conclusion**:
The distance between the two lenses in normal adjustment is \( L = 98 \, \text{cm} \).

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

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