A convex lens of power +2.5`D` is in contact with a concave lens of focal length 25 cm. The power of combination is

Options

A. `-1.5D`
B. 0 D
C. `+1.5D`
D. `+6.5D`

Answer

To solve the problem, we need to find the power of the combination of a convex lens and a concave lens that are in contact with each other.

### Step-by-Step Solution:

1. **Identify the power of the convex lens**:
- The power of the convex lens (P1) is given as +2.5 D (diopters).

2. **Find the focal length of the concave lens**:
- The focal length (F2) of the concave lens is given as 25 cm.
- Since the concave lens has a negative focal length, we convert this to meters:
\[ F2 = -25 \text{ cm} = -0.25 \text{ m} \]

3. **Calculate the power of the concave lens**:
- The power (P2) of a lens is given by the formula:
\[ P = \frac{1}{F} \quad \text{(in meters)} \]
- For the concave lens:
\[ P2 = \frac{1}{F2} = \frac{1}{-0.25} = -4 \text{ D} \]

4. **Calculate the total power of the combination**:
- The total power (P_total) of two lenses in contact is the sum of their powers:
\[ P_{\text{total}} = P1 + P2 \]
- Substituting the values:
\[ P_{\text{total}} = 2.5 + (-4) = 2.5 - 4 = -1.5 \text{ D} \]

5. **Interpret the result**:
- The negative sign indicates that the combination behaves like a concave lens. Therefore, the power of the combination is -1.5 D.

### Final Answer:
The power of the combination of the lenses is **-1.5 D**.

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