Question

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\mathring{A}$ and ${\lambda }_2=5000\mathring{A}$ then ratio of their respective resolving powers(corresponding to ${\lambda }_1$ and ${\lambda }_2$) is

• A. 16:25
• B. 9:1
• C. 4:5
• D. 5:4

Answer 1

The correct option is D 5:4

We know,

$ResolvingPower\propto \frac{1}{\lambda }$

Given,

${\lambda }_1=4000\mathring{A}$

${\lambda }_2=5000\mathring{A}$

$\Rightarrow \frac{R{P}_{{\lambda }_1}}{R{P}_{{\lambda }_2}}=\frac{{\lambda }_2}{{\lambda }_1}$

$\Rightarrow \frac{R{P}_{{\lambda }_1}}{R{P}_{{\lambda }_2}}=\frac{5000}{4000}=\frac{5}{4}$

$\Rightarrow R{P}_{{\lambda }_1}:R{P}_{{\lambda }_2}=5:4$

Hence, the correct answer is OPTION D.