When an object is viewed with a light of wavelength `6000Å` under a microscope, its resolving power is `10^(4)`. The resolving power of the microscope when the same object is viewed with a light of wavelength `4000Å`, is `nxx10^(3)`. The vlaue of n is

Answer

To solve the problem, we need to understand the relationship between the resolving power of a microscope and the wavelength of light used. The resolving power (R) of a microscope is inversely proportional to the wavelength (λ) of the light used. This can be expressed mathematically as:

\[ R \propto \frac{1}{\lambda} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Wavelength 1 (λ₁) = 6000 Å
- Resolving power 1 (R₁) = \( 10^4 \)
- Wavelength 2 (λ₂) = 4000 Å
- Resolving power 2 (R₂) = \( n \times 10^3 \)

2. **Use the Proportionality Relationship:**
From the relationship \( R \propto \frac{1}{\lambda} \), we can write:
\[ \frac{R_2}{R_1} = \frac{\lambda_1}{\lambda_2} \]

3. **Substitute the Known Values:**
Substitute the known values into the equation:
\[ \frac{R_2}{10^4} = \frac{6000}{4000} \]

4. **Simplify the Right Side:**
Simplifying \( \frac{6000}{4000} \):
\[ \frac{6000}{4000} = \frac{6}{4} = \frac{3}{2} \]

5. **Set Up the Equation:**
Now we can set up the equation:
\[ \frac{R_2}{10^4} = \frac{3}{2} \]

6. **Solve for R₂:**
Multiply both sides by \( 10^4 \):
\[ R_2 = \frac{3}{2} \times 10^4 \]

7. **Convert R₂ to the Required Form:**
To express \( R_2 \) in the form \( n \times 10^3 \):
\[ R_2 = 1.5 \times 10^4 = 15 \times 10^3 \]

8. **Identify the Value of n:**
From the equation \( R_2 = n \times 10^3 \), we can see that:
\[ n = 15 \]

### Final Answer:
The value of \( n \) is **15**.