A lens of power `6` D is put in contact with a lens of power `-4` D. The combination will behave like a

Options

A. divergent lens of focal length `25` cm
B. convergent lens of focal length `50` cm
C. divergent lens of focal length `20` cm
D. convergent lens of focal length `100` cm

Explanation

To solve the problem, we need to find the combined power of the two lenses and determine the nature of the combination.

### Step-by-Step Solution:

1. **Identify the Powers of the Lenses**:
- The power of the first lens (P1) is +6 D (diopters).
- The power of the second lens (P2) is -4 D.

2. **Calculate the Combined Power**:
- The formula for the combined power (P) of two lenses in contact is:
\[ P = P1 + P2 \]
- Substituting the values:
\[ P = 6 \, D + (-4 \, D) = 6 \, D - 4 \, D = 2 \, D \]

3. **Determine the Focal Length**:
- The relationship between power (P) and focal length (f) is given by:
\[ P = \frac{1}{f} \]
- Rearranging this gives us:
\[ f = \frac{1}{P} \]
- Substituting the combined power:
\[ f = \frac{1}{2} \, m = 0.5 \, m \]

4. **Convert Focal Length to Centimeters**:
- To express the focal length in centimeters, we multiply by 100:
\[ f = 0.5 \, m \times 100 = 50 \, cm \]

5. **Determine the Nature of the Lens**:
- Since the focal length is positive (50 cm), this indicates that the combination behaves like a convergent lens or a convex lens.

### Final Conclusion:
The combination of the two lenses behaves like a convergent lens with a focal length of 50 cm.

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