Question

When an object is viewed with a light of wavelength $6000\mathring{A}$ under a microscope, its resolving power is ${10}^4$. The resolving power of the microscope when the same object is viewed with a light of wavelength $4000\mathring{A}$, is:

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

Answer 1

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

The resolving power of microscope is given by the following formula.
$R=\frac{2\mu \sin \theta }{1.22\lambda }$
where, $\mu =$ refractive index
$\lambda =$ wavelength of the height
$\therefore R\propto \frac{1}{\lambda }$
$\frac{R_2}{R_1}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{6000}{4000}\stackrel{o}{A}$
$R_2=\frac{3}{2}\times R_1=\frac{3}{2}\times {10}^4$
$=1.5\times {10}^4$.