Question

A telescope $T$, has objective of diameter $100\text{inch}$ and the wavelength of light used for this telescope is $5000A^{\circ }$. Another telescope $T_2$ has objective of diameter $50\text{inch}$ and the wavelength of light used for this telescope is $6000A^{\circ }$. If $P_1,P_2$ represents the resolving powers of $T_1$ and $T_2$ respectively whereas $\Delta {\theta }_1,\Delta {\theta }_2$ represents the limit of resolutions of $T_1$ and $T_2$ respectively, then choose the correct option (s).

• A. $\frac{P_1}{P_2}=\frac{5}{12}$
• B. $\frac{\Delta {\theta }_1}{\Delta {\theta }_2}=\frac{5}{12}$
• C. $\frac{P_1}{P_2}=\frac{12}{5}$
• D. $\frac{\Delta {\theta }_1}{\Delta {\theta }_2}=\frac{12}{5}$

Answer 1

Answer: (B), (C)

$\frac{P_1}{P_2}=\frac{12}{5}$

The resolving power of telescope
$P=\frac{b}{1.22\lambda }$

$\Rightarrow \frac{P_1}{P_2}=\frac{b_1}{b_2}\times \frac{{\lambda }_2}{{\lambda }_1}=\frac{100}{50}\times \frac{6000}{5000}$

$\therefore \frac{P_1}{P_2}=\frac{12}{5}$

As limit of resolution,

$\theta \propto \frac{1}{\text{Resolving Power}}$

$\therefore \frac{\Delta {\theta }_1}{\Delta {\theta }_2}=\frac{P_2}{P_1}=\frac{5}{12}$

Hence, options $\left(B\right)$ and $\left(C\right)$ are correct.