Question

When an object is viewed using light of wavelength $6000\mathring{\text{A}}$ 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 $4000\mathring{\text{A}}$?

• A. $1.5\times {10}^4$
• B. $2\times {10}^4$
• C. $3.2\times {10}^4$
• D. $3\times {10}^4$

Answer 1

The correct option is A $1.5\times {10}^4$

The resolving power of a microscope is given by the formula

$R=\frac{2\mu \sin \theta }{1.22\lambda }$

$\Rightarrow R\propto \frac{1}{\lambda }$.

$\Rightarrow \frac{R_1}{R_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{4000}{6000}=\frac{2}{3}$

$R_2=R_1\times \frac{3}{2}={10}^4\times \frac{3}{2}=1.5\times {10}^4$

Hence, $\left(A\right)$ is the correct answer.