Question

When wavelength of light used in optical instruments A and B are 4500Å and 6000Å respectively, the ratio of resolving power of A to B will be

• A. 16 : 9
• B. 7 : 1
• C. 9 : 16
• D. 4 : 3

Hint:

The resolving power of an optical instrument is inversely proportional to the wavelength of light. A shorter wavelength means higher resolving power.

Answer 1

The Correct Option is D

Step 1: Understanding resolving power.
The resolving power \( R \) of an optical instrument is inversely proportional to the wavelength \( \lambda \) of the light used. This means that the instrument with a smaller wavelength will have a greater resolving power.
Step 2: Calculating the ratio.
Let \( R_A \) and \( R_B \) be the resolving powers of instruments A and B, respectively. We have: \[ \frac{R_A}{R_B} = \frac{\lambda_B}{\lambda_A} \] Substitute the values for \( \lambda_A \) and \( \lambda_B \): \[ \frac{R_A}{R_B} = \frac{6000}{4500} = \frac{4}{3} \]
Step 3: Conclusion.
The ratio of the resolving power of A to B is \( 4 : 3 \), hence the correct answer is (D) 4 : 3.