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(B) The intensity of reflected light is minimum when the angle of incidence is the Brewster's angle $(i_B)$.At Brewster's angle,the reflected ray is c

Vedclass · Accepted Answer

$13\, m, 27\, m$

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(B) The intensity of reflected light is minimum when the angle of incidence is the Brewster's angle $(i_B)$.At Brewster's angle,the reflected ray is completely polarized.Given $\mu = 	an i_B = \frac{4}{3}$.From the geometry of the problem,let the point of reflection on the river be $A$. The person is at point $C$ at height $10\, m$ and the light source is at point $E$ at height $Y$ on the tower.In $	riangle ABC$,$	an(90^{\circ} - i_B) = \frac{BC}{AB} \implies \cot i_B = \frac{10}{X}$.Since $	an i_B = \frac{4}{3}$,we have $\cot i_B = \frac{3}{4}$.Thus,$\frac{3}{4} = \frac{10}{X} \implies X = \frac{40}{3} \approx 13.33\, m$.In $	riangle AEF$,$	an(90^{\circ} - i_B) = \frac{EF}{AF} \implies \cot i_B = \frac{Y}{50 - X}$.Substituting the values,$\frac{3}{4} = \frac{Y}{50 - 13.33} = \frac{Y}{36.67}$.$Y = \frac{3}{4} 	imes 36.67 \approx 27.5\, m$.Rounding to the nearest values,$X \approx 13\, m$ and $Y \approx 27\, m$.

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