A nearsighted person cannot clearly see beyond 200 cm. Find the power of the lens needed to see objects at large distances.

Answer

To solve the problem of finding the power of the lens needed for a nearsighted person who cannot see beyond 200 cm, we will follow these steps:

### Step 1: Understand the given information
- The person cannot see objects clearly beyond 200 cm, which means their far point is at 200 cm (or -2 m when converted to meters, since the convention is to take the distance of virtual images as negative).
- The object distance (u) for distant objects is considered to be at infinity (u = ∞).

### Step 2: Use the lens formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Where:
- \( f \) = focal length of the lens
- \( v \) = image distance (for the nearsighted person, this is -2 m)
- \( u \) = object distance (for distant objects, this is ∞)

### Step 3: Substitute values into the lens formula
Substituting the known values into the lens formula:
\[ \frac{1}{f} = \frac{1}{-2} - \frac{1}{\infty} \]
Since \( \frac{1}{\infty} = 0 \), the equation simplifies to:
\[ \frac{1}{f} = \frac{1}{-2} \]

### Step 4: Solve for the focal length (f)
From the equation:
\[ f = -2 \text{ m} \]
This negative sign indicates that the lens is a diverging lens.

### Step 5: Calculate 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 \( f \):
\[ P = \frac{1}{-2} = -0.5 \text{ diopters} \]

### Final Answer
The power of the lens needed for the nearsighted person to see objects at large distances is \( -0.5 \) diopters.

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