A convergent lens of power 8 D is combined with a divergent lens of power `- 10 D`. Calculate focal length of the combination.

Explanation

To solve the problem of finding the focal length of a combination of a convergent lens and a divergent lens, we can follow these steps:

### Step 1: Identify the Powers of the Lenses
- The power of the convergent lens (P1) is given as \( +8 \, D \).
- The power of the divergent lens (P2) is given as \( -10 \, D \).

### Step 2: Calculate the Total Power of the Combination
- The total power (P) of the combination of lenses is the sum of the individual powers:
\[ P = P1 + P2 = 8 \, D + (-10 \, D) = 8 - 10 = -2 \, D \]

### Step 3: Relate Power to Focal Length
- The power of a lens is related to its focal length (f) by the formula:
\[ P = \frac{1}{f} \]
- Rearranging this formula to find the focal length gives:
\[ f = \frac{1}{P} \]

### Step 4: Substitute the Total Power into the Focal Length Formula
- Substituting the total power into the formula:
\[ f = \frac{1}{-2 \, D} \]
- This gives:
\[ f = -0.5 \, m \]

### Step 5: Convert Focal Length to Centimeters
- Since the focal length is often expressed in centimeters, we convert meters to centimeters:
\[ f = -0.5 \, m \times 100 \, \frac{cm}{m} = -50 \, cm \]

### Final Answer
- The focal length of the combination of the convergent and divergent lenses is \( -50 \, cm \).

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