A person has been using speetacles of power `-1.0` Dioptre for distant vision and a separate reading glass of power `2.0` Dioptres.What is the least distance of distinct vision for this person:

Options

A. `10cm`
B. `40cm`
C. `30cm`
D. `50cm`

Answer

To solve the problem, we need to find the least distance of distinct vision for a person who uses spectacles with a power of -1.0 Dioptres for distant vision and a reading glass with a power of +2.0 Dioptres.

### Step-by-Step Solution:

1. **Understanding the Powers of Lenses**:
- The power of a lens (P) is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length in meters.
- For the spectacles, we have:
\[ P_{spectacles} = -1.0 \, \text{D} \quad \Rightarrow \quad f_{spectacles} = -1 \, \text{m} = -100 \, \text{cm} \]
- For the reading glass, we have:
\[ P_{reading \, glass} = +2.0 \, \text{D} \quad \Rightarrow \quad f_{reading \, glass} = +0.5 \, \text{m} = +50 \, \text{cm} \]

2. **Using the Lens Formula**:
- The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
- Here, \( u \) is the object distance (which we will take as the least distance of distinct vision, denoted as \( -x \)), and \( v \) is the image distance.

3. **Considering the Spectacles**:
- For the spectacles, the least distance of distinct vision \( x \) can be calculated as follows:
\[ \frac{1}{v} - \frac{1}{(-x)} = \frac{1}{-100} \]
- Rearranging gives:
\[ -\frac{1}{x} = -\frac{1}{100} \quad \Rightarrow \quad \frac{1}{x} = \frac{1}{100} \]
- Thus, we find:
\[ x = 100 \, \text{cm} \]

4. **Considering the Reading Glass**:
- The reading glass will help the person see objects closer. The effective near point with the reading glass can be calculated as:
\[ \frac{1}{v} - \frac{1}{(-x)} = \frac{1}{50} \]
- Rearranging gives:
\[ -\frac{1}{x} = -\frac{1}{50} \quad \Rightarrow \quad \frac{1}{x} = \frac{1}{50} \]
- Thus, we find:
\[ x = 50 \, \text{cm} \]

5. **Final Calculation**:
- The least distance of distinct vision for this person, considering both the spectacles and the reading glass, is:
\[ x = 50 \, \text{cm} \]

### Conclusion:
The least distance of distinct vision for this person is **50 cm**.