The Question is from neet-physics , and it was created by the author ABDUL JILANI BASHA

Question

The ratio of resolving powers of an optical microscope for two wavelengths and ${\lambda _1} = 4000{A^ \circ }$ and ${\lambda _2} = 6000\,{A^ \circ }$ is

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
	**Primary Concept**: Resolving power of an optical microscope.
	**Related Topics**: Wavelength of light, diffraction.
	**Prerequisites**: Understanding that resolving power is inversely proportional to wavelength.
## SOLUTION PATHWAY
**Given Information**:
	Wavelength 1:  $\lambda_1 = 4000 	ext{ Å}$
	Wavelength 2:  $\lambda_2 = 6000 	ext{ Å}$
**Method & Steps**:
	1.  Recall the relationship between resolving power (RP) and wavelength ($\lambda$):  Resolving Power (RP) is inversely proportional to wavelength ($\lambda$ ). This can be expressed as $RP \propto \frac{1}{\lambda}$.
		Reasoning: A smaller wavelength allows for resolving smaller details.
		Formula/Rule: $RP \propto \frac{1}{\lambda}$
	2. Set up the ratio of resolving powers for the two wavelengths:
		Working: $\frac{RP_1}{RP_2} = \frac{1/\lambda_1}{1/\lambda_2} = \frac{\lambda_2}{\lambda_1}$
		Key Point: The resolving power ratio is the inverse of the wavelength ratio.
	3. Substitute the given values and calculate the ratio:
		Working: $\frac{RP_1}{RP_2} = \frac{6000}{4000} = \frac{6}{4} = \frac{3}{2}$
		Result: The ratio of resolving powers is 3:2.
		Verification: The calculated ratio matches option D.
## OPTION ANALYSIS
[A] :x: Incorrect. This ratio likely results from a mistake in squaring or inverting the wavelengths incorrectly.
[B] :x: Incorrect. This ratio doesn't represent the correct inverse relationship between resolving power and wavelength.
[C] :x: Incorrect. This ratio might result from directly squaring the inverse of the wavelength ratio.
[D] ✓: Correct. The ratio of resolving powers is the inverse ratio of the wavelengths: 6000/4000 = 3/2.
## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Directly using the ratio of wavelengths instead of the inverse ratio. [How to avoid]: Remember that resolving power is inversely proportional to the wavelength.
		2. [Error 2]: Squaring the wavelengths or taking their square roots while calculating the ratio. [How to avoid]: The resolving power is directly proportional to 1/wavelength and not any other function of wavelength. 
	**Quick Tips**:
		1. [Helpful shortcut]: Directly use the ratio of wavelengths in reverse order. $RP_1/RP_2 = \lambda_2/\lambda_1$
		2. [Memory aid]: Remember that smaller the wavelength, the better the resolving power, hence the inverse relationship.

ABDUL JILANI BASHA · Answer

$16:{\rm{ }}81$

ABDUL JILANI BASHA · Answer

$8:{\rm{ }}27$

ABDUL JILANI BASHA · Answer

$9:{\rm{ }}4$

ABDUL JILANI BASHA · Answer

The correct Option is "$3:{\rm{ }}2$"

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