Question

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\stackrel{o}{A}$ and ${\lambda }_2=5000\stackrel{o}{A}$, 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

Answer: (D)

$5:4$

Resolving Power (R.P) :It is the reciprocal of resolving limit<br>

$R.P.=\frac{1}{d\theta }$

For a Telescope : Resolving limit,

$d\theta$ $=$ $\frac{1.22\times \lambda }{a}$

$\therefore R.P.\propto \frac{1}{\lambda }$

Where $\lambda$ = wavelength of light used to illuminate the object.

$a$ =aperture of the objective.

Given: ${\lambda }_1=4000A$ and ${\lambda }_2=5000A$

$R.P.|\propto \frac{1}{\lambda }|\Rightarrow \frac{(R.P.{)}_1}{(R.P.{)}_2}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{5}{4}$