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

Options

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

Explanation

To solve the problem, we need to use the concept of resolution in optics, which is given by the formula:

\[ x \propto \lambda \]

This means that the limit of resolution (x) is directly proportional to the wavelength (λ) of the light used. Therefore, we can set up a proportion between the two scenarios given in the question.

### Step-by-step Solution:

1. **Identify the known values:**
- Distance between the two points that can just be resolved with the first wavelength (λ1 = 6000 Å) is \( x_1 = 0.1 \, \text{mm} \).
- The second wavelength (λ2 = 4800 Å) is what we need to find the new limit of resolution \( x_2 \).

2. **Set up the proportion:**
\[ \frac{x_1}{x_2} = \frac{\lambda_1}{\lambda_2} \]
Substituting the known values:
\[ \frac{0.1 \, \text{mm}}{x_2} = \frac{6000 \, \text{Å}}{4800 \, \text{Å}} \]

3. **Convert wavelengths to the same unit:**
Since \( 1 \, \text{Å} = 10^{-7} \, \text{mm} \), we can convert the wavelengths:
- \( \lambda_1 = 6000 \, \text{Å} = 6000 \times 10^{-7} \, \text{mm} \)
- \( \lambda_2 = 4800 \, \text{Å} = 4800 \times 10^{-7} \, \text{mm} \)

4. **Calculate the ratio:**
\[ \frac{6000}{4800} = \frac{6000 \div 2400}{4800 \div 2400} = \frac{2.5}{2} = 1.25 \]

5. **Substitute back into the proportion:**
\[ \frac{0.1}{x_2} = 1.25 \]

6. **Cross-multiply to solve for \( x_2 \):**
\[ 0.1 = 1.25 \cdot x_2 \]
\[ x_2 = \frac{0.1}{1.25} = 0.08 \, \text{mm} \]

### Final Answer:
The limit of resolution when using light of wavelength \( 4800 \, \text{Å} \) becomes \( 0.08 \, \text{mm} \).