KCET · Physics · Ray Optics
Two poles are separated by a distance of \(3.14 \mathrm{~m}\). The resolving power of human eye is \(1 \mathrm{~min}\) of an arc. The maximum distance from which he can identify the two poles distinctly is
- A \(10.8 \mathrm{~km}\)
- B \(5.4 \mathrm{~km}\)
- C \(188 \mathrm{~m}\)
- D \(376 \mathrm{~m}\)
Answer & Solution
Correct Answer
(A) \(10.8 \mathrm{~km}\)
Step-by-step Solution
Detailed explanation
Given, distance between poles \((d)=3.14 \mathrm{~m}\)
Resoolving power \(=1\) min or \(1^{\prime}\)
Let maximum distance of two poles from eye to be resolved distinctly be \(x\). Then, angle on eye in minute for two poles can be found using figure given below
\(\theta=\frac{d}{x} \times \frac{180}{\pi} \times 60\)
\(\Rightarrow \quad 1=\frac{3.14}{x} \times \frac{180}{\pi} \times 60\)
\(\Rightarrow \quad x=\frac{3.14 \times 180 \times 60}{\pi}=10794.5\)
\(=10.8 \mathrm{~km}\)
Resoolving power \(=1\) min or \(1^{\prime}\)
Let maximum distance of two poles from eye to be resolved distinctly be \(x\). Then, angle on eye in minute for two poles can be found using figure given below
\(\theta=\frac{d}{x} \times \frac{180}{\pi} \times 60\)
\(\Rightarrow \quad 1=\frac{3.14}{x} \times \frac{180}{\pi} \times 60\)
\(\Rightarrow \quad x=\frac{3.14 \times 180 \times 60}{\pi}=10794.5\)
\(=10.8 \mathrm{~km}\)
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