The eyepiece of a refracting telescope has f = 9 cm. In the normal setting, separation betweeen objective and eyepiece is 1.8 m. Find the magnification

Options

A. 20
B. 19
C. 18
D. 21

Explanation

To find the magnification of the refracting telescope, we can follow these steps:

### Step 1: Identify the given values
- Focal length of the eyepiece (f_e) = 9 cm = 0.09 m
- Separation between the objective and eyepiece (L) = 1.8 m

### Step 2: Use the formula for the separation in a telescope
In a refracting telescope, the separation between the objective and the eyepiece is given by the formula:
\[ L = f_o + f_e \]
where \( f_o \) is the focal length of the objective.

### Step 3: Rearrange the formula to find the focal length of the objective
We can rearrange the equation to find \( f_o \):
\[ f_o = L - f_e \]
Substituting the known values:
\[ f_o = 1.8 \, \text{m} - 0.09 \, \text{m} \]
\[ f_o = 1.71 \, \text{m} \]

### Step 4: Calculate the magnification
The magnification (M) of a telescope is given by the formula:
\[ M = -\frac{f_o}{f_e} \]
Substituting the values we found:
\[ M = -\frac{1.71 \, \text{m}}{0.09 \, \text{m}} \]
\[ M = -19 \]

### Step 5: Interpret the result
Since magnification is typically expressed as a positive value in this context, we can say:
\[ M = 19 \]

### Final Answer
The magnification of the refracting telescope is **19**.

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