Question

The ratio of resolving powers of an optical microscope for two wavelengths λ₁ = 4000 Å and λ₂ = 6000 Å is

• A. 8 : 27
• B. 9 : 4
• C. 3 : 2
• D. 16 : 81

Answer 1

The Correct Option is C

To find the ratio of resolving powers of an optical microscope for two different wavelengths, we use the principle that the resolving power (R.P) of a microscope is inversely proportional to the wavelength (\( \lambda \)) of light used. Mathematically, this is expressed as:

\text{R.P} \propto \frac{1}{\lambda}

Therefore, the resolving powers for two different wavelengths, \( \lambda_1 \) and \( \lambda_2 \), can be compared as follows:

\frac{\text{R.P}_1}{\text{R.P}_2} = \frac{\lambda_2}{\lambda_1}

Given:

• \( \lambda_1 = 4000 \, \text{Å} \)
• \( \lambda_2 = 6000 \, \text{Å} \)

Substituting these values into the equation:

\frac{\text{R.P}_1}{\text{R.P}_2} = \frac{6000}{4000} = \frac{3}{2}

Thus, the ratio of the resolving powers for the wavelengths \( 4000 \, \text{Å} \) and \( 6000 \, \text{Å} \) is 3:2.

Among the provided options, 3:2 is the correct answer.

Conclusion:

The ratio of resolving powers of an optical microscope for the given wavelengths is 3:2. This is because, according to the formula for resolving power, the power is inversely proportional to the wavelength, resulting in a higher resolving power for shorter wavelengths.