A person cannot see objects clearly that are closer that 1 m and farther than 5 m. To correct the eye vision, the person will use

Options

A. Bifocal lenses of power -3 D and +0.2 D
B. Bifocal lenses of power -2.5 D and +3.5 D
C. Bifocal lenses of power -1.5 D and +5D
D. Bifocal lenses of power -0.2 D and +3D

Answer

To solve the problem, we need to determine what kind of corrective lens the person should use based on their vision limitations. The person cannot see objects clearly that are closer than 1 meter (the near point) and farther than 5 meters (the far point).

### Step-by-Step Solution:

1. **Identify the Vision Problem**:
- The person has a near point of 1 meter and a far point of 5 meters. This means they can only see objects clearly between these two distances.

2. **Determine the Type of Lens Needed**:
- Since the person cannot see objects closer than 1 meter, they need a lens that allows them to see objects that are closer. This typically indicates the need for a **convex lens** (or converging lens), which can help focus light from nearby objects onto the retina.

3. **Calculate the Focal Length**:
- To find the focal length of the lens required, we can use the lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
- Here, \( v \) is the image distance (which we want to set at 1 meter for clear vision), and \( u \) is the object distance (which can be less than 1 meter).

4. **Set Up the Equation**:
- For an object placed at a distance of \( u \) (let's say 0.5 m for calculation):
\[ v = 1 \, \text{m}, \quad u = -0.5 \, \text{m} \, (\text{object distance is negative in lens formula}) \]
- Plugging these values into the lens formula:
\[ \frac{1}{f} = \frac{1}{1} - \frac{1}{-0.5} \]
- This simplifies to:
\[ \frac{1}{f} = 1 + 2 = 3 \implies f = \frac{1}{3} \, \text{m} \approx 0.33 \, \text{m} \]

5. **Conclusion**:
- The person will need a **convex lens** with a focal length of approximately 0.33 meters (or 33 cm) to correct their vision so they can see objects clearly that are closer than 1 meter.