A nearsighted person cannot see beyond 25 cm. Assuming that the separation of the glass from the eye is 1 cm, find the power of lens needed to see distant objects.

Answer

To find the power of the lens needed for a nearsighted person who cannot see beyond 25 cm, we can follow these steps:

### Step 1: Understand the Problem
A nearsighted person can see objects clearly only up to a certain distance (25 cm in this case). To see distant objects (considered to be at infinity), they need a corrective lens.

### Step 2: Determine the Image Distance
The image formed by the corrective lens should be at the near point of the eye, which is 25 cm from the eye. However, since the lens is 1 cm away from the eye, the image distance (v) from the lens will be:
\[ v = 25 \, \text{cm} - 1 \, \text{cm} = 24 \, \text{cm} \]

### Step 3: Sign Convention
According to the sign convention for lenses:
- Distances measured in the direction of the incident light (towards the lens) are negative.
- Distances measured in the opposite direction (away from the lens) are positive.

Since the image is formed on the same side as the object (the lens), we take:
\[ v = -24 \, \text{cm} \]

### Step 4: Object Distance
For distant objects, we can consider the object distance (u) to be at infinity:
\[ u = -\infty \]

### Step 5: Apply the Lens Formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Substituting the values:
\[ \frac{1}{f} = \frac{1}{-24 \, \text{cm}} + \frac{1}{-\infty} \]
Since \( \frac{1}{-\infty} = 0 \), we have:
\[ \frac{1}{f} = \frac{1}{-24} \]
Thus, the focal length \( f \) is:
\[ f = -24 \, \text{cm} \]

### Step 6: Convert Focal Length to Meters
Convert the focal length from centimeters to meters:
\[ f = -24 \, \text{cm} = -0.24 \, \text{m} \]

### Step 7: Calculate the Power of the Lens
The power \( P \) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
Substituting the focal length in meters:
\[ P = \frac{1}{-0.24} \approx -4.17 \, \text{D} \]
Rounding off, we can say:
\[ P \approx -4.2 \, \text{D} \]

### Final Answer
The power of the lens needed to see distant objects is approximately **-4.2 diopters**.

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