A farsighted person cannot see objects placed closer to 50 cm. Find the power of the lens needed to see the objects at 20 cm.

Answer

To solve the problem of finding the power of the lens needed for a farsighted person to see objects at 20 cm, we can follow these steps:

### Step 1: Understand the Problem
A farsighted person cannot see objects closer than 50 cm. We need to determine the power of a lens that allows this person to see objects at a distance of 20 cm.

### Step 2: Define the Variables
- The object distance (u) is -20 cm (the negative sign indicates that the object is on the same side as the incoming light).
- The image distance (v) is -50 cm (the negative sign indicates that the image is formed on the same side as the object for a virtual image).

### Step 3: Use the Lens Formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
We will substitute the values of \(u\) and \(v\) into this formula.

### Step 4: Substitute the Values
Substituting \(u = -20\) cm and \(v = -50\) cm into the lens formula:
\[ \frac{1}{f} = \frac{1}{-50} - \frac{1}{-20} \]

### Step 5: Calculate the Right Side
Calculating the right side:
\[ \frac{1}{f} = -\frac{1}{50} + \frac{1}{20} \]
To combine these fractions, find a common denominator (which is 100):
\[ \frac{1}{f} = -\frac{2}{100} + \frac{5}{100} = \frac{3}{100} \]

### Step 6: Solve for Focal Length (f)
Now, we can find \(f\):
\[ f = \frac{100}{3} \text{ cm} \]

### Step 7: Calculate the Power of the Lens
The power \(P\) of a lens is given by the formula:
\[ P = \frac{1}{f} \text{ (in meters)} \]
First, convert \(f\) from cm to meters:
\[ f = \frac{100}{3} \text{ cm} = \frac{100}{3 \times 100} \text{ m} = \frac{1}{3} \text{ m} \]
Now, calculate the power:
\[ P = \frac{1}{\frac{1}{3}} = 3 \text{ diopters} \]

### Conclusion
The power of the lens needed for the farsighted person to see objects at 20 cm is **+3 diopters**.

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