Question

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\mathring{\text{A}}$ and ${\lambda }_2=5000\mathring{\text{A}}$, the 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 $5:4$

${\lambda }_1=4000\mathring{\text{A}}$
${\lambda }_2=5000\mathring{\text{A}}$

For any optical instrument (microscope or telescope),
Resolving power $\propto \frac{1}{\lambda }$

$\Rightarrow \frac{(RP{)}_1}{(RP{)}_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{5000}{4000}=\frac{5}{4}$

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