A far sighted person cannot see object clearly al a distance less than 75 cm from his eyes. The power of the lens needed to read an object al 25 cm is

Options

A. `+1.50 D`
B. `+2.67 D`
C. `-2.67 d`
D. `-1.50 d`

Answer

To solve the problem of finding the power of the lens needed for a far-sighted person to read an object at 25 cm, we will follow these steps:

### Step 1: Understand the problem
A far-sighted person has a near point (the closest distance at which they can see clearly) of 75 cm. They want to read an object that is 25 cm away. We need to determine the power of the lens required to enable them to see the object clearly at this distance.

### Step 2: Identify the relevant formula
We will use the lens formula to find the focal length (f) of the lens needed:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where:
- \( v \) is the image distance (the near point of the person, which is -75 cm),
- \( u \) is the object distance (the distance to the object they want to read, which is -25 cm).

### Step 3: Substitute the values into the lens formula
Substituting the values into the lens formula:
\[ \frac{1}{f} = \frac{1}{-75} - \frac{1}{-25} \]

### Step 4: Simplify the equation
Calculating the right side:
\[ \frac{1}{f} = -\frac{1}{75} + \frac{1}{25} \]
Finding a common denominator (which is 75):
\[ \frac{1}{f} = -\frac{1}{75} + \frac{3}{75} = \frac{2}{75} \]

### Step 5: Calculate the focal length
Now, we can find \( f \):
\[ f = \frac{75}{2} = 37.5 \text{ cm} \]

### Step 6: Calculate the power of the lens
The power (P) of the lens is given by the formula:
\[ P = \frac{100}{f} \text{ (in cm)} \]
Substituting \( f = 37.5 \) cm:
\[ P = \frac{100}{37.5} \approx 2.67 \text{ diopters} \]

### Step 7: Conclusion
The power of the lens needed for the far-sighted person to read an object at 25 cm is approximately +2.67 diopters.

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