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 is given as \( +2.5 \, D \).

2. **Calculate the Focal Length of the Concave Lens:**
- The focal length of the concave lens is given as \( 25 \, cm \).
- Since it is a concave lens, its focal length will be negative:
\[ F_2 = -25 \, cm \]

3. **Convert the Focal Length of the Concave Lens to Power:**
- The formula for power \( P \) in terms of focal length \( F \) is:
\[ P = \frac{1}{F} \quad \text{(in meters)} \]
- First, convert the focal length from centimeters to meters:
\[ F_2 = -25 \, cm = -0.25 \, m \]
- Now, calculate the power of the concave lens:
\[ P_2 = \frac{1}{-0.25} = -4 \, D \]

4. **Calculate the Total Power of the Combination:**
- The total power \( P_{eq} \) of the combination of lenses in contact is the algebraic sum of their individual powers:
\[ P_{eq} = P_1 + P_2 \]
- Substitute the values:
\[ P_{eq} = 2.5 \, D + (-4 \, D) = 2.5 \, D - 4 \, D = -1.5 \, D \]

5. **Conclusion:**
- The power of the combination of the convex lens and the concave lens is:
\[ P_{eq} = -1.5 \, D \]

### Final Answer:
The power of the combination is \( -1.5 \, D \).

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