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JEE Mains · Physics · STD 12 - Wave optics
- JEE Mains 2013
- Hard
- MCQ
A person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \( \simeq \frac{4}{3})\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(13\,m, 27\, m\)
Step-by-step Solution
Detailed explanation
case of Booster angle where reflected and refracted ray both become polarized. So,
\({\mu _1} = \tan {i_B} = \frac{4}{3}\)
From triangle \(ABC,\)
\(\tan (90 - {i_B}) = \frac{{BC}}{{AB}}\)
\(\cot {\mkern 1mu} {i_B} = \frac{{10}}{x}\)
\(\frac{3}{4} = \frac{{10}}{x}\)
\(x = \frac{{40}}{3} = 13{\mkern 1mu} \,m\)
From triangle \(AEF,\)
\(\tan (90 - {i_B}) = \frac{y}{{50 - x}}\)
\(\cot {i_B} = \frac{y}{{50 - 13}}\)
\(\frac{3}{4} = \frac{y}{{37}}\)
\(y=27\;m\)
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