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 fo

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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

TestHub · Accepted Answer

The resolving power of a microscope is given by the formula:

$RP = \frac{2 μ sin θ}{λ}$

This shows that the resolving power is inversely proportional to the wavelength of the light used:

$RP \propto \frac{1}{λ}$

The ratio of the resolving power for $λ_{1}$ to that for $λ_{2}$ is:

$\frac{R P _{1}}{R P _{2}} = \frac{λ _{2}}{λ _{1}}$

Substituting the given values $λ_{1} = 6800$ and $λ_{2} = 5100$ :

$\frac{R P _{1}}{R P _{2}} = \frac{5100}{6800} = \frac{51}{68} = \frac{3}{4}$

The ratio is $3 : 4$ .

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