Question

In an optical instrument- microscope, the wavelength of light used are \(λ_1 = 6800\) Å and \(λ_2 = 5100\) Å. The ratio of the resolving power of microscope corresponding to '\(λ_1\)' to that for '\(λ_2\)' is

• A. \(9:16\)
• B. \(5:4\)
• C. \(4:3\)
• D. \(3:4\)

Hint:

Resolving power of a microscope is proportional to 1 / lambda.

Answer 1

The Correct Option is D

Step 1: Cancel the common factors:
Both measurements use the same microscope, so only $\lambda$ changes. Resolving power is $\propto 1/\lambda$.

Step 2: Simplify the numbers:
$\dfrac{5100}{6800} = \dfrac{51}{68} = \dfrac{3}{4}$, since $51 = 3\times17$ and $68 = 4\times17$.

Step 3: Interpret:
Red-end light (6800 Å) resolves less well than green-blue light (5100 Å), so the first number in the ratio must be smaller.

Final Answer:
Option (D). \[ \boxed{3:4 \text{ (D)}} \]