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, eyepiece, and inverting lens of a terrestrial telescope at normal adjustment, we can use the following formula:

**Step 1: Write down the formula for the length of the tube.**
The formula to calculate the length of the tube (L) is given by:
\[ L = f_0 + f_e + 4f_i \]
where:
- \( f_0 \) = focal length of the objective lens
- \( f_e \) = focal length of the eyepiece
- \( f_i \) = focal length of the inverting lens

**Step 2: Substitute the given values into the formula.**
From the question, we have:
- \( f_0 = 20 \, \text{cm} \) (focal length of the objective)
- \( f_e = 10 \, \text{cm} \) (focal length of the eyepiece)
- \( f_i = 5 \, \text{cm} \) (focal length of the inverting lens)

Now substituting these values into the formula:
\[ L = 20 \, \text{cm} + 10 \, \text{cm} + 4 \times 5 \, \text{cm} \]

**Step 3: Calculate the value of \( 4f_i \).**
Calculating \( 4f_i \):
\[ 4f_i = 4 \times 5 \, \text{cm} = 20 \, \text{cm} \]

**Step 4: Add all the components together.**
Now, add all the values together:
\[ L = 20 \, \text{cm} + 10 \, \text{cm} + 20 \, \text{cm} \]
\[ L = 50 \, \text{cm} \]

**Step 5: State the final answer.**
Thus, the length of the tube containing the lenses at normal adjustment is:
\[ \text{Length of the tube} = 50 \, \text{cm} \]

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