The focal length of a lens of power – 2D is :

Options

A. + 50 cm
B. - 50 cm
C. + 2 cm
D. - 2 cm.

Answer

To find the focal length of a lens given its power, we can use the relationship between power (P) and focal length (f). The formula is given by:

\[ P = \frac{1}{f} \]

where:
- P is the power of the lens in diopters (D),
- f is the focal length in meters (m).

### Step-by-Step Solution:

1. **Identify the given power of the lens:**
- The power of the lens is given as \( P = -2D \).

2. **Use the formula to find the focal length:**
- Rearranging the formula \( P = \frac{1}{f} \) gives us:
\[ f = \frac{1}{P} \]
- Substituting the value of P:
\[ f = \frac{1}{-2} \]

3. **Calculate the focal length:**
- Performing the calculation:
\[ f = -0.5 \text{ meters} \]

4. **Convert the focal length to centimeters:**
- Since \( 1 \text{ meter} = 100 \text{ centimeters} \):
\[ f = -0.5 \times 100 = -50 \text{ centimeters} \]

5. **Interpret the result:**
- The negative sign indicates that the lens is a diverging lens (concave lens).

### Final Answer:
The focal length of a lens of power -2D is **-50 centimeters**.