There is a symmetric bi-convex lens and it is cut in two equal parts by a plane passing through the centre of lens and perpendicular to its principal axis. If power of original lens is 10 D then what will be the power of each part of the lens ?

Options

A. 10 D
B. 20 D
C. 5 D
D. 2.5 D

Explanation

To solve the problem, we need to determine the power of each half of a symmetric bi-convex lens after it has been cut into two equal parts. The original lens has a power of 10 diopters.

### Step-by-Step Solution:

1. **Understanding the Power of the Lens**:
The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length of the lens in meters. Given that the power of the original lens is 10 D, we can find the focal length:
\[ P = 10 \, \text{D} \implies f = \frac{1}{P} = \frac{1}{10} = 0.1 \, \text{m} \]

2. **Cutting the Lens**:
When the symmetric bi-convex lens is cut into two equal halves by a plane passing through the center and perpendicular to the principal axis, each half will still retain the same curvature but will now act as a plano-convex lens.

3. **Calculating the New Power**:
For each half of the lens, the new configuration can be analyzed. The focal length of a plano-convex lens can be derived from the lens maker's formula:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Here, for the plano-convex lens:
- \( R_1 = R \) (the radius of curvature of the convex side)
- \( R_2 = \infty \) (the flat side)

Therefore, the formula simplifies to:
\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R} - 0 \right) = (n - 1) \frac{1}{R} \]

4. **Using the Original Lens Power**:
For the original lens:
\[ \frac{1}{f} = (n - 1) \left( \frac{2}{R} \right) = 10 \]
This means:
\[ n - 1 = \frac{10R}{2} = 5R \]

5. **Finding the Power of Each Half**:
Now, substituting \( n - 1 \) back into the formula for the half-lens:
\[ \frac{1}{f'} = (n - 1) \frac{1}{R} = 5R \cdot \frac{1}{R} = 5 \]
Thus, the power of each half-lens is:
\[ P' = \frac{1}{f'} = 5 \, \text{D} \]

### Final Answer:
The power of each part of the lens after cutting is **5 diopters**.