A person suffering from defective vision can see objects clearly only beyond 100 cm from the eye. Find the power of lens required so that he can see clearly the object placed at a distance of distinct vision (D = 25cm)

Options

A. 2D
B. 3D
C. `-2D`
D. `-3D`

Answer

To solve the problem of finding the power of the lens required for a person with defective vision, we will follow these steps:

### Step 1: Understand the problem
The person can see objects clearly only beyond 100 cm. This means that the far point of the person’s vision is at 100 cm. We need to find the power of a lens that will allow this person to see an object placed at a distance of 25 cm clearly.

### Step 2: Define the variables
- The distance at which the person can see clearly (far point), \( v = -100 \) cm (negative because it's a virtual image for the lens).
- The distance of the object (near point), \( u = -25 \) cm (also negative as per sign convention).

### Step 3: Use the lens formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Substituting the values of \( v \) and \( u \):
\[ \frac{1}{f} = \frac{1}{-100} - \frac{1}{-25} \]

### Step 4: Simplify the equation
Calculating the right side:
\[ \frac{1}{f} = -\frac{1}{100} + \frac{1}{25} \]
Finding a common denominator (which is 100):
\[ \frac{1}{f} = -\frac{1}{100} + \frac{4}{100} = \frac{3}{100} \]

### Step 5: Calculate the focal length
Now, we can find \( f \):
\[ f = \frac{100}{3} \text{ cm} \approx 33.33 \text{ cm} \]

### Step 6: Convert focal length to meters
To convert cm to meters:
\[ f \approx 0.3333 \text{ m} \]

### Step 7: Calculate the power of the lens
The power \( P \) of a lens is given by:
\[ P = \frac{1}{f} \text{ (in meters)} \]
Substituting the value of \( f \):
\[ P = \frac{1}{0.3333} \approx 3 \text{ D} \]

### Conclusion
The power of the lens required for the person to see clearly at 25 cm is approximately \( 3 \text{ D} \).