Focal length of objective eye piece and inverting lens of a terrestrial telescope are 20 cm, 10 cm and 5 cm respectively. Length of the tube containing these lenses at normal adjustment is

Options

A. 30 cm
B. 35 cm
C. 50 cm
D. 40 cm

Answer

To find the length of the tube containing the objective lens, inverting lens, and eyepiece of a terrestrial telescope at normal adjustment, we can follow these steps:

### Step 1: Understand the components of the telescope
A terrestrial telescope consists of three main components:
- Objective lens (focal length \( f_0 \))
- Inverting lens (focal length \( f_i \))
- Eyepiece (focal length \( f_e \))

Given:
- Focal length of the objective lens, \( f_0 = 20 \, \text{cm} \)
- Focal length of the inverting lens, \( f_i = 5 \, \text{cm} \)
- Focal length of the eyepiece, \( f_e = 10 \, \text{cm} \)

### Step 2: Determine the length of the tube at normal adjustment
At normal adjustment, the length of the telescope tube can be calculated using the formula:
\[ L = f_0 + 4f_i + f_e \]

### Step 3: Substitute the values into the formula
Now, substitute the given values into the formula:
\[ L = 20 \, \text{cm} + 4 \times 5 \, \text{cm} + 10 \, \text{cm} \]

### Step 4: Calculate the values
First, calculate \( 4 \times 5 \):
\[ 4 \times 5 = 20 \, \text{cm} \]

Now substitute this back into the equation:
\[ L = 20 \, \text{cm} + 20 \, \text{cm} + 10 \, \text{cm} \]

### Step 5: Add the values together
Now, add the values:
\[ L = 20 + 20 + 10 = 50 \, \text{cm} \]

### Conclusion
The length of the tube containing these lenses at normal adjustment is \( 50 \, \text{cm} \).