A person cannot see objects clearly beyond 125 cm. The power of the lens to correct the vision is

Options

A. `-2D`
B. `+2D`
C. `-0.8D`
D. `+0.8D`

Answer

To solve the problem of determining the power of the lens needed to correct a person's vision, we can follow these steps:

### Step 1: Understanding the Problem
The person can see objects clearly only up to 125 cm. This means that their far point (the farthest point they can see clearly) is at 125 cm. For a normal vision, the far point is at infinity. Therefore, we need to find a lens that will allow this person to see objects at infinity clearly.

### Step 2: Setting Up the Lens Formula
We will use the lens formula:
\[ \frac{1}{F} = \frac{1}{B} - \frac{1}{U} \]
where:
- \( F \) = focal length of the lens
- \( B \) = image distance (the distance where the image is formed)
- \( U \) = object distance (the distance of the object from the lens)

### Step 3: Assigning Values
In this case:
- The object is at infinity, so \( U = -\infty \) (the negative sign indicates that the object is on the same side as the incoming light).
- The image distance \( B \) should be at the person's far point, which is \( -125 \) cm (the negative sign indicates that the image is formed on the same side as the object).

### Step 4: Applying the Values to the Lens Formula
Substituting the values into the lens formula:
\[ \frac{1}{F} = \frac{1}{-125} - \frac{1}{-\infty} \]
Since \( \frac{1}{-\infty} = 0 \), the equation simplifies to:
\[ \frac{1}{F} = \frac{1}{-125} \]
Thus, we find:
\[ F = -125 \text{ cm} \]

### Step 5: Converting Focal Length to Meters
To calculate the power of the lens, we need the focal length in meters:
\[ F = -1.25 \text{ m} \quad (\text{since } -125 \text{ cm} = -1.25 \text{ m}) \]

### Step 6: Calculating the Power of the Lens
The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{F} \text{ (in meters)} \]
Substituting the value of \( F \):
\[ P = \frac{1}{-1.25} = -0.8 \text{ diopters} \]

### Step 7: Conclusion
The power of the lens required to correct the person's vision is:
\[ P = -0.8 \text{ diopters} \]
Since the power is negative, this indicates that a concave lens is needed for correction.

### Final Answer
The power of the lens to correct the vision is \(-0.8\) diopters.

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