When an object is viewed using light of wavelength $6000 ˚ A$ under a microscope, the resolving power of the microscope is $10^{4}$ . Find the resolving power of the microscope, when the same object is viewed using light of wavelength $4000 ˚ A$ ?

1.5 \times 10^{4}

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2 \times 10^{4}

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3.2 \times 10^{4}

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3 \times 10^{4}

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Solution

The correct option is A $1.5 \times 10^{4}$
The resolving power of a microscope is given by the formula

$R = \frac{2 μ sin θ}{1.22 λ}$

$\Rightarrow R \propto \frac{1}{λ}$ .

$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{4000}{6000} = \frac{2}{3}$

$R_{2} = R_{1} \times \frac{3}{2} = 10^{4} \times \frac{3}{2} = 1.5 \times 10^{4}$

Hence, $(A)$ is the correct answer.

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