Q143 / 160 · TS EAMCET 2024 (09 May Shift 2) · Physics
The diameter of the objective of a telescope is 3.6 m . The limit of resolution of the telescope for a light of wavelength 540 nm is
- A$1.22 \times 10^{-7} \mathrm{rad}$
- Correct answerB$1.83 \times 10^{-7} \mathrm{rad}$
- C$0.61 \times 10^{-7} \mathrm{rad}$
- D$3.76 \times 10^{-7} \mathrm{rad}$
Solution
Given,
Diameter of the objective, $\mathrm{d}=3.6 \mathrm{~m}$ wavelength of light, $\lambda=540 \times 10^{-9} \mathrm{~m}$ Resolving limit, $\mathrm{d} \theta=\frac{1.22 \lambda}{\mathrm{~d}}$
$\begin{aligned}
& \mathrm{d} \theta=\frac{1.22 \times 540 \times 10^{-9}}{3.6}=183 \times 10^{-9} \\
& =1.83 \times 10^{-7} \mathrm{rad} .
\end{aligned}$
Hence, the correct answer is option: 'B'.