There is symmetric bi-convex lens and it is cut in two pieces by a plane containing principal axis. If power of the original lens is 10 D then what will be the power of each part ?

Options

A. 10 D
B. 5 D
C. 20 D
D. 40 D

Explanation

To solve the problem, we need to analyze the effect of cutting a symmetric bi-convex lens into two halves along a plane containing the principal axis.

### Step-by-Step Solution:

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

2. **Cutting the Lens**:
When the symmetric bi-convex lens is cut into two equal halves along the principal axis, each half retains the same radius of curvature and the same focal length as the original lens.

3. **Analyzing Each Half**:
Since the two halves are symmetric and identical, they will each have the same focal length \( f \) as the original lens. Therefore, the power of each half can be calculated using the same power formula:
\[ P_{\text{half}} = \frac{1}{f} \]

4. **Calculating the Power of Each Half**:
Since cutting the lens does not change the focal length, the power of each half remains the same as that of the original lens:
\[ P_{\text{half}} = 10 \, D \]

5. **Conclusion**:
Therefore, the power of each part of the lens after cutting remains \( 10 \) diopters.

### Final Answer:
The power of each part of the lens is \( 10 \, D \).

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