Two points separated by a distance of 0.1 mm can just be resolved in a microscope when a light of wavelength 6000 Å is used. If the light of wavelength 4800 Å is used this limit of resolution becomes :-

Options

A. `0.08`mm
B. `0.10`mm
C. `0.12`mm
D. `0.06mm`

Explanation

To solve the problem, we need to understand the relationship between the limit of resolution in a microscope and the wavelength of light used. The limit of resolution (d) is directly proportional to the wavelength (λ) of the light used. This relationship can be expressed mathematically as:

\[ d \propto \lambda \]

This means that if we have two different wavelengths, we can set up a ratio to find the new limit of resolution when the wavelength changes.

### Step-by-step solution:

1. **Identify the known values:**
- Initial limit of resolution (d1) = 0.1 mm
- Initial wavelength (λ1) = 6000 Å
- New wavelength (λ2) = 4800 Å

2. **Set up the proportional relationship:**
Since the limit of resolution is directly proportional to the wavelength, we can write:
\[ \frac{d_1}{d_2} = \frac{\lambda_1}{\lambda_2} \]
Where:
- \(d_1\) = initial limit of resolution
- \(d_2\) = new limit of resolution we want to find
- \(\lambda_1\) = initial wavelength
- \(\lambda_2\) = new wavelength

3. **Substitute the known values into the equation:**
\[ \frac{0.1 \text{ mm}}{d_2} = \frac{6000 \text{ Å}}{4800 \text{ Å}} \]

4. **Cross-multiply to solve for \(d_2\):**
\[ 0.1 \text{ mm} \cdot 4800 \text{ Å} = d_2 \cdot 6000 \text{ Å} \]

5. **Calculate \(d_2\):**
\[ d_2 = \frac{0.1 \text{ mm} \cdot 4800 \text{ Å}}{6000 \text{ Å}} \]

6. **Perform the calculation:**
- First, simplify the right side:
\[ d_2 = 0.1 \cdot \frac{4800}{6000} \]
- Calculate \(\frac{4800}{6000} = 0.8\):
\[ d_2 = 0.1 \cdot 0.8 = 0.08 \text{ mm} \]

7. **Final result:**
The new limit of resolution when using light of wavelength 4800 Å is:
\[ d_2 = 0.08 \text{ mm} \]

### Answer:
The limit of resolution becomes 0.08 mm.