Question

When an object is viewed with a light of wavelength \( 6000 \,\text{\AA} \) under a microscope its resolving power is \( 10^4 \). The resolving power of the microscope when the same object is viewed with a light of wavelength \( 4000 \,\text{\AA} \) is

• A. $10^4$
• B. $2 \times 10^4$
• C. $3\sqrt{2} \times 10^4$
• D. $3 \times 10^4$
• E. $1.5 \times 10^4$

Hint:

Resolving power $\propto \frac{1}{\lambda}$ → smaller wavelength gives sharper image.

Answer 1

Answer: (E)

Concept: Resolving power of microscope
\[ \text{Resolving power} \propto \frac{1}{\lambda} \] ---

Step 1: Relation \[ \frac{RP_1}{RP_2} = \frac{\lambda_2}{\lambda_1} \] ---

Step 2: Substitute values \[ RP_2 = RP_1 \cdot \frac{\lambda_1}{\lambda_2} \] \[ RP_2 = 10^4 \cdot \frac{6000}{4000} \] ---

Step 3: Simplify \[ RP_2 = 10^4 \cdot \frac{3}{2} = 1.5 \times 10^4 \] --- Physical Insight:
• Smaller wavelength → better resolution
• Hence resolving power increases --- Final Answer: \[ \boxed{1.5 \times 10^4} \]