The numerical aperture of an objective of a microscope is `0.5` and the wavelength of light used is `5000 A^(0)`. Its limit of resolution will be

Options

A. `6.1xx 10^(7)m`
B. `6.1xx 10^(-7)m`
C. `6.1xx 10^(-4)m`
D. `6.1xx 10^(4)m`

Answer

To find the limit of resolution of a microscope given the numerical aperture and the wavelength of light, we can use the formula for the limit of resolution (r):

### Step-by-Step Solution:

1. **Identify the given values:**
- Numerical Aperture (NA) = 0.5
- Wavelength of light (λ) = 5000 Å (angstroms)

2. **Convert the wavelength from angstroms to meters:**
- 1 Å = \(10^{-10}\) meters
- Therefore, \(5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m}\)

3. **Use the formula for the limit of resolution:**
\[ r = \frac{\lambda}{2 \times \text{NA}} \]

4. **Substitute the values into the formula:**
\[ r = \frac{5 \times 10^{-7} \, \text{m}}{2 \times 0.5} \]

5. **Simplify the denominator:**
\[ 2 \times 0.5 = 1 \]
So, the equation simplifies to:
\[ r = \frac{5 \times 10^{-7} \, \text{m}}{1} = 5 \times 10^{-7} \, \text{m} \]

6. **Final result:**
The limit of resolution \( r \) is \( 5 \times 10^{-7} \, \text{m} \).