The eyepice of an astronomicasl telescope has a focasl length of 10 cm. The telescope is focussed for normal vision of distant objects when the tube length is 1.0 m. find the focal length of the bjective and the magnifying power of the telescope.

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas for an astronomical telescope.

### Step 1: Identify the Given Information
- Focal length of the eyepiece (Fe) = 10 cm
- Length of the telescope (L) = 1 m = 100 cm

### Step 2: Relate the Focal Lengths to the Length of the Telescope
For an astronomical telescope, the relationship between the focal lengths of the objective lens (Fo) and the eyepiece (Fe) and the length of the telescope (L) is given by the equation:
\[ L = Fo + Fe \]

### Step 3: Rearrange the Equation to Find Fo
We can rearrange the equation to solve for the focal length of the objective lens (Fo):
\[ Fo = L - Fe \]

### Step 4: Substitute the Known Values
Now, substitute the known values into the equation:
\[ Fo = 100 \, \text{cm} - 10 \, \text{cm} \]
\[ Fo = 90 \, \text{cm} \]

### Step 5: Calculate the Magnifying Power of the Telescope
The magnifying power (M) of an astronomical telescope is given by the formula:
\[ M = \frac{Fo}{Fe} \]

### Step 6: Substitute the Focal Lengths into the Magnifying Power Formula
Now, substitute the values of Fo and Fe into the magnifying power formula:
\[ M = \frac{90 \, \text{cm}}{10 \, \text{cm}} \]
\[ M = 9 \]

### Final Answers
- Focal length of the objective lens (Fo) = 90 cm
- Magnifying power of the telescope (M) = 9

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