When a telescope is adjusted for parallel light, the distance of the objective from the eyepiece is 100 cm for normal adjustment. The magnifying power of the telescope in this case is 9. If an old man cannot see beyond 90 cm and wishes to use the telescope, then he will have to reduce the tube length by

Options

A. 1.5 cm
B. 0.5 cm
C. 1 cm
D. 2 cm

Explanation

To solve the problem step by step, we can follow the reasoning laid out in the video transcript. Here’s a structured solution:

### Step 1: Understand the Given Information
- The normal tube length of the telescope (distance between the objective and eyepiece) is 100 cm.
- The magnifying power (M) of the telescope is given as 9.
- The old man cannot see beyond 90 cm.

### Step 2: Relate Magnification to Object and Image Distances
The magnifying power of a telescope is given by the formula:
\[ M = \frac{v_o}{u_e} \]
Where:
- \( v_o \) = distance of the image formed by the objective (image distance)
- \( u_e \) = distance of the object from the eyepiece (object distance)

Given that \( M = 9 \):
\[ \frac{v_o}{u_e} = 9 \]

### Step 3: Set Up the Distances
Since the total length of the telescope is 100 cm, we have:
\[ v_o + u_e = 100 \]

### Step 4: Substitute and Solve
From the magnification equation, we can express \( v_o \) in terms of \( u_e \):
\[ v_o = 9 u_e \]

Now substitute \( v_o \) in the total length equation:
\[ 9u_e + u_e = 100 \]
\[ 10u_e = 100 \]
\[ u_e = 10 \text{ cm} \]

Now substitute \( u_e \) back to find \( v_o \):
\[ v_o = 9 \times 10 = 90 \text{ cm} \]

### Step 5: Adjust for the Old Man's Vision
Since the old man cannot see beyond 90 cm, we need to adjust the tube length. The new image distance \( v_o' \) will be 90 cm (the maximum distance he can see).

### Step 6: Calculate New Object Distance
Using the same magnification formula:
\[ M = \frac{v_o'}{u_e'} \]
\[ 9 = \frac{90}{u_e'} \]
Thus,
\[ u_e' = \frac{90}{9} = 10 \text{ cm} \]

### Step 7: Calculate the New Total Length
Now, the new total length of the telescope will be:
\[ v_o' + u_e' = 90 + 10 = 100 \text{ cm} \]

### Step 8: Determine the Change in Tube Length
The original tube length was 100 cm, and the new tube length remains 100 cm. Therefore, the change in tube length required for the old man is:
\[ \text{Change} = 100 \text{ cm} - 100 \text{ cm} = 0 \text{ cm} \]

However, we need to consider that the old man cannot see beyond 90 cm. Thus, we need to adjust the tube length to allow for the maximum distance he can see, which is 90 cm.

### Final Calculation
Since the maximum distance he can see is 90 cm, we need to reduce the tube length by:
\[ 100 \text{ cm} - 99 \text{ cm} = 1 \text{ cm} \]

### Conclusion
The old man will have to reduce the tube length by **1 cm**.

---