A person can not see the objects clearly placed at a distance more than 40 cm . He is advised to use a lens of power

Options

A. `- 2.5 D`
B. `+ 2.5 D`
C. `- 6.25 D`
D. `+ 1.5 D`

Answer

To solve the problem, we need to determine the power of the lens required for a person who cannot see objects clearly beyond a distance of 40 cm. This condition indicates that the person is suffering from myopia (nearsightedness).

### Step-by-Step Solution:

1. **Identify the Condition**:
The person cannot see objects clearly beyond 40 cm, which indicates that their far point is 40 cm. This means they can only see objects clearly up to this distance.

2. **Understanding Myopia**:
Myopia is a condition where distant objects appear blurry. To correct this, a concave lens is used, which helps in diverging the light rays so that they appear to come from a point closer than the actual object.

3. **Focal Length Calculation**:
The focal length (f) of the lens needed can be related to the far point (D) using the formula:
\[ f = -D \]
Here, D is the far point in meters. Since the far point is given as 40 cm, we convert this to meters:
\[ D = 40 \, \text{cm} = 0.40 \, \text{m} \]
Therefore, the focal length is:
\[ f = -0.40 \, \text{m} \]

4. **Calculating Power of the Lens**:
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where f is in meters. Substituting the value of f:
\[ P = \frac{1}{-0.40} = -2.5 \, \text{diopters} \]

5. **Conclusion**:
The power of the lens required for the person to see clearly is -2.5 diopters. This negative sign indicates that it is a concave lens, which is appropriate for correcting myopia.

### Final Answer:
The person is advised to use a lens of power -2.5 diopters.

---