A person can see clearly upto 1 m. The nature and power of the lens which will enable him to see things at a distance of 3 m is

Options

A. concave, -0.66 D
B. convex, -0.66 D
C. concave, -0.33D
D. convex, -0.33D

Explanation

To solve the problem, we need to determine the nature and power of the lens required for a person who can see clearly up to 1 meter to see objects at a distance of 3 meters. Here’s a step-by-step solution:

### Step 1: Identify the Given Information
- The maximum distance at which the person can see clearly (the near point) is \( d_{near} = 1 \, \text{m} \).
- The distance at which the person wants to see clearly (the far point) is \( d_{far} = 3 \, \text{m} \).

### Step 2: Set Up the Lens Formula
We will use the lens formula, which is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( f \) is the focal length of the lens,
- \( v \) is the image distance,
- \( u \) is the object distance.

### Step 3: Assign Values to \( u \) and \( v \)
- Since the object is at 3 meters, we have \( u = -3 \, \text{m} \) (the object distance is taken as negative in lens formula convention).
- The image must be formed at the near point of the person, so \( v = 1 \, \text{m} \).

### Step 4: Substitute Values into the Lens Formula
Now, substituting the values into the lens formula:
\[ \frac{1}{f} = \frac{1}{1} - \frac{1}{-3} \]
This simplifies to:
\[ \frac{1}{f} = 1 + \frac{1}{3} = 1 + 0.333 = \frac{4}{3} \]

### Step 5: Calculate the Focal Length
Now, we can find \( f \):
\[ f = \frac{3}{4} \, \text{m} = 0.75 \, \text{m} \]

### Step 6: Calculate the Power of the Lens
The power \( P \) of the lens is given by:
\[ P = \frac{1}{f(\text{in meters})} \]
Substituting \( f = 0.75 \, \text{m} \):
\[ P = \frac{1}{0.75} = \frac{4}{3} \approx 1.33 \, \text{D} \]

### Step 7: Determine the Nature of the Lens
Since the power is positive, this indicates that the lens is a **convex lens**.

### Final Answer
The nature of the lens is **convex**, and the power of the lens is approximately **1.33 diopters**.

---