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Question

If the wavelength of light used is doubled, the resolving power of a microscope will be:

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Resolving Power of a Microscope
	**Related Topics**: Diffraction, Wavelength of Light, Optics
	**Prerequisites**: Understanding of the relationship between resolving power and wavelength.
## SOLUTION PATHWAY
**Given Information**:
	Wavelength of light is doubled.
**Method & Steps**:
	1. **Recall the formula for resolving power**:  The resolving power (R) of a microscope is given by $R = \frac{\lambda}{2NA}$, where $\lambda$ is the wavelength of light and NA is the numerical aperture.  Since NA is a property of the lens and remains constant, the resolving power is directly proportional to the wavelength.
	Reasoning: A smaller wavelength leads to better resolution (smaller resolvable distance).
	Formula/Rule: $R \propto \lambda$
	2. **Analyze the effect of doubling the wavelength**: If the wavelength ($\lambda$) is doubled (i.e., $\lambda' = 2\lambda$), the new resolving power (R') becomes $R' = \frac{2\lambda}{2NA} = 2R$.
	Working: $R' = 2 	imes \frac{\lambda}{2NA} = 2R$
	Key Point: Resolving power is directly proportional to the wavelength used.
	3. **Determine the change in resolving power**: The new resolving power (R') is twice the original resolving power (R).
	Result: The resolving power is doubled.
	Verification: The direct proportionality between wavelength and resolving power confirms the result.
## OPTION ANALYSIS
[A] :x: Halved: Incorrect. Resolving power is directly proportional, not inversely proportional, to the wavelength.  If wavelength increases, resolving power increases.
[B] ✓: Doubled: Correct. Doubling the wavelength doubles the resolving power.
[C] :x: Quadrupled: Incorrect.  The relationship is linear, not squared.  Doubling the wavelength doubles, not quadruples, the resolving power.
[D] :x: Unchanged: Incorrect.  The resolving power is directly dependent on the wavelength. Changing the wavelength will change the resolving power.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing resolving power with magnification: Magnification simply enlarges the image; resolving power determines the clarity and detail.
			How to avoid: Remember that resolving power is about distinguishing between two closely spaced objects, while magnification is about increasing the apparent size of the image.
		2. Forgetting the direct proportionality:  Incorrectly assuming an inverse relationship between wavelength and resolving power.
			How to avoid: Memorize the formula $R = \frac{\lambda}{2NA}$ and understand its implications.
	**Quick Tips**:
		1. Shorter wavelength = Better resolution:  Electron microscopes use electron beams with shorter wavelengths than light, achieving much higher resolution.
		2.  $R \propto \lambda$:  Remember the direct proportionality for quick assessments.

Mr. ANIL KUMAR.G · Answer

Halved

Mr. ANIL KUMAR.G · Answer

The correct Option is "Doubled"

Mr. ANIL KUMAR.G · Answer

Quadrupled

Mr. ANIL KUMAR.G · Answer

Unchanged

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