The value of numerical aperature of the objective lens of a microscope is 1.25 if light of wavelength 5000 Å is used the minimum separation between two points to be seen as distinct, will be

Options

A. 0.24 `mum`
B. `0.38mum`
C. `0.12mum`
D. `0.48mum`

Answer

To solve the problem of finding the minimum separation between two points that can be seen as distinct using a microscope with a numerical aperture (NA) of 1.25 and light of wavelength 5000 Å, we can follow these steps:

### Step 1: Understand the Formula for Minimum Separation
The minimum separation \( d \) between two points that can be resolved is given by the formula:
\[ d = \frac{\lambda}{2 \cdot NA} \]
where:
- \( d \) is the minimum separation,
- \( \lambda \) is the wavelength of light used,
- \( NA \) is the numerical aperture of the lens.

### Step 2: Convert Wavelength to Meters
The wavelength given is in angstroms (Å). We need to convert this to meters for consistency in units.
\[ 1 \, \text{Å} = 10^{-10} \, \text{m} \]
Thus,
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### Step 3: Substitute Values into the Formula
Now we can substitute the values of \( \lambda \) and \( NA \) into the formula:
\[ d = \frac{5 \times 10^{-7} \, \text{m}}{2 \cdot 1.25} \]

### Step 4: Calculate the Denominator
Calculate the denominator:
\[ 2 \cdot 1.25 = 2.5 \]

### Step 5: Calculate the Minimum Separation
Now substitute back into the equation:
\[ d = \frac{5 \times 10^{-7}}{2.5} = 2 \times 10^{-7} \, \text{m} \]

### Step 6: Convert Back to Angstroms (if needed)
To express the minimum separation in angstroms:
\[ d = 2 \times 10^{-7} \, \text{m} = 2 \times 10^{10} \, \text{Å} = 2000 \, \text{Å} \]

### Final Answer
The minimum separation between two points to be seen as distinct is:
\[ d = 2000 \, \text{Å} \]

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