To solve the problem, we need to determine the spectacles required for reading (for the near point) and for seeing distant objects (for the far point).
### Step-by-Step Solution:
1. **Identify the Near Point and Far Point:**
- The near point of the person is given as \( D_{near} = 50 \, \text{cm} \) (0.5 m).
- The far point of the person is given as \( D_{far} = 1.5 \, \text{m} \).
2. **Calculate the Focal Length for Reading (Near Point):**
- For reading, the person needs to see objects clearly at a distance of \( V = 25 \, \text{cm} \) (the standard near point for a normal vision).
- The object distance \( U \) is the near point of the person, which is \( U = -50 \, \text{cm} \) (negative because it is on the same side as the object).
- Using the lens formula:
\[
\frac{1}{F} = \frac{1}{V} - \frac{1}{U}
\]
Substituting the values:
\[
\frac{1}{F} = \frac{1}{25} - \frac{1}{-50}
\]
\[
\frac{1}{F} = \frac{1}{25} + \frac{1}{50}
\]
Finding a common denominator (50):
\[
\frac{1}{F} = \frac{2}{50} + \frac{1}{50} = \frac{3}{50}
\]
Therefore,
\[
F = \frac{50}{3} \, \text{cm} \approx 16.67 \, \text{cm}
\]
3. **Calculate the Power of the Lens for Reading:**
- The power \( P \) of the lens is given by:
\[
P = \frac{1}{F(\text{in meters})}
\]
Converting \( F \) to meters:
\[
F = \frac{50}{3} \, \text{cm} = \frac{50}{300} \, \text{m} = \frac{1}{6} \, \text{m}
\]
Thus,
\[
P = \frac{1}{\frac{1}{6}} = 6 \, \text{D} \quad \text{(positive for converging lens)}
\]
4. **Calculate the Focal Length for Distant Objects (Far Point):**
- For distant objects, we consider \( V = \infty \) and \( U = -1.5 \, \text{m} \).
- Using the lens formula again:
\[
\frac{1}{F} = \frac{1}{V} - \frac{1}{U}
\]
Substituting the values:
\[
\frac{1}{F} = 0 - \frac{1}{-1.5}
\]
Therefore,
\[
\frac{1}{F} = \frac{1}{1.5} \Rightarrow F = 1.5 \, \text{m}
\]
5. **Calculate the Power of the Lens for Distant Objects:**
- Converting \( F \) to meters:
\[
P = \frac{1}{F} = \frac{1}{1.5} \approx 0.67 \, \text{D} \quad \text{(negative for diverging lens)}
\]
### Final Results:
- The spectacles required for reading (near point) is approximately **+6 D**.
- The spectacles required for seeing distant objects (far point) is approximately **-0.67 D**.
