Light of wavelength `5,000 Å` is used in a microscope of numerical aperture 0.10. Calculate the resovlving power of the microscope.

Answer

To calculate the resolving power of the microscope, we can follow these steps:

### Step 1: Understand the formula for resolving power
The resolving power \( R \) of a microscope is given by the formula:
\[ R = \frac{2 \mu \sin \theta}{1.22 \lambda} \]
where:
- \( \mu \sin \theta \) is the numerical aperture (NA) of the microscope,
- \( \lambda \) is the wavelength of light used.

### Step 2: Identify the given values
From the problem, we have:
- Wavelength \( \lambda = 5000 \) Å (angstroms),
- Numerical aperture \( \mu \sin \theta = 0.10 \).

### Step 3: Convert the wavelength to meters
Since the wavelength is given in angstroms, we need to convert it to meters:
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m}. \]

### Step 4: Substitute the values into the formula
Now, substituting the values into the resolving power formula:
\[ R = \frac{2 \times 0.10}{1.22 \times 5 \times 10^{-7}}. \]

### Step 5: Calculate the denominator
First, calculate the denominator:
\[ 1.22 \times 5 \times 10^{-7} = 6.1 \times 10^{-7}. \]

### Step 6: Calculate the resolving power
Now substitute this back into the formula for \( R \):
\[ R = \frac{0.20}{6.1 \times 10^{-7}}. \]

### Step 7: Perform the division
Calculating the division:
\[ R = \frac{0.20}{6.1 \times 10^{-7}} = \frac{20 \times 10^{-1}}{6.1 \times 10^{-7}} = \frac{20}{6.1} \times 10^{6} \approx 3.2787 \times 10^{5} \, \text{m}^{-1}. \]

### Step 8: Round the final answer
Rounding the answer gives:
\[ R \approx 3.3 \times 10^{5} \, \text{m}^{-1}. \]

### Final Answer
The resolving power of the microscope is approximately \( 3.3 \times 10^{5} \, \text{m}^{-1} \).

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