Two lenses of power 6 D and – 2 D are combined to form a single lens. The focal length of this lens will be

Options

A. `3/2 m`
B. `1/4m`
C. `4m`
D. `1/8 m`

Answer

To find the focal length of the combined lens made from two lenses with powers of 6 D and -2 D, we can follow these steps:

### 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 -2 D.

2. **Calculate the Equivalent Power**:
- When two lenses are combined in parallel, the total power (P) is the sum of the individual powers:
\[ P = P1 + P2 \]
- Substituting the values:
\[ P = 6 D + (-2 D) = 6 D - 2 D = 4 D \]

3. **Calculate the Focal Length**:
- The focal length (f) of a lens is related to its power (P) by the formula:
\[ f = \frac{1}{P} \]
- Substituting the equivalent power:
\[ f = \frac{1}{4 D} \]
- Since 1 D = 1 m⁻¹, we convert the power into focal length:
\[ f = \frac{1}{4} \text{ meters} = 0.25 \text{ meters} \]

4. **Final Answer**:
- The focal length of the combined lens is 0.25 meters.