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A post of height 4 m is dipped straight in a pond. 1 m of the post remains above the water of the pond. If the rays of the sun are inclined at an angle of 45^(@) to the surface of water what will be the length of the shadow of the post at the bottom of the pond? Refractive index of water mu = (4)/(3). |
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Answer» Solution :When the vessel is EMPTY, a light ray from the point A enters the telescope T following the straight path AO [Fig. 2.55]. When the vessel is filled with the liquid, aray of light from the point B moves along BO and after refraction in air enters the telescope. Let h be the height of the vessel. `"Here" angleBOC = i and angleAOC = r` According to the FIGURE, `(sini)/(sinr) = (1)/(mu) or, mu = (sinr)/(sini)` `or, "" 1.5 = ((AC)/(AO))/((BC)/(BO)) = (AC)/(AO) xx (BO)/(BC) = (AC)/(BC) xx (BO)/(AO)` `or, "" 1.5 = (10)/(5) xx (sqrt(BC^(2) + CO^(2)))/(sqrt(AC^(2) + CO^(2))) = 2 xx (sqrt(25 + h^(2)))/(sqrt(100 + h^(2)))` `or, " " 2.25 = (4(25 + h^(2)))/(100 + h^(2))` `or, "" h = 8.45 cm` 
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