The focal length of the objective of a terrestrial telescope is 80 cm and it is adjusted for parallel rays, then its magnifying power is 20. If the focal length of erecting lens is 20 cm , then full length of telescope will be

Options

A. 164cm
B. 124cm
C. 100cm
D. 100cm

Explanation

To find the full length of the terrestrial telescope, we will follow these steps:

### Step 1: Understand the components of the telescope
The full length of a terrestrial telescope is given by the formula:
\[ \text{Length of telescope} = f_o + f_e + 4f_e' \]
where:
- \( f_o \) = focal length of the objective lens
- \( f_e \) = focal length of the eyepiece lens
- \( f_e' \) = focal length of the erecting lens

### Step 2: Identify the given values
From the question:
- Focal length of the objective lens, \( f_o = 80 \, \text{cm} \)
- Magnifying power, \( M = 20 \)
- Focal length of the erecting lens, \( f_e' = 20 \, \text{cm} \)

### Step 3: Calculate the focal length of the eyepiece
The magnifying power of a telescope is given by the formula:
\[ M = \frac{f_o}{f_e} \]
Rearranging this gives us:
\[ f_e = \frac{f_o}{M} \]
Substituting the known values:
\[ f_e = \frac{80 \, \text{cm}}{20} = 4 \, \text{cm} \]

### Step 4: Substitute the values into the length formula
Now, we can substitute \( f_o \), \( f_e \), and \( f_e' \) into the length formula:
\[ \text{Length of telescope} = f_o + f_e + 4f_e' \]
\[ \text{Length of telescope} = 80 \, \text{cm} + 4 \, \text{cm} + 4 \times 20 \, \text{cm} \]
Calculating \( 4 \times 20 \):
\[ 4 \times 20 = 80 \, \text{cm} \]

Now substituting back:
\[ \text{Length of telescope} = 80 \, \text{cm} + 4 \, \text{cm} + 80 \, \text{cm} \]
\[ \text{Length of telescope} = 164 \, \text{cm} \]

### Final Answer
The full length of the telescope is \( 164 \, \text{cm} \).

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