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Physics – Geometrical Optics-A man is looking down a 9 m deep tank filled with a transparent liquid of refractive index √3 . The line of sight of the man makes an angle of 30° with the horizontal. What is the apparent depth of the tank as seen by the man?
Real Depth of the tank = 9 m.Refractive Index of the liquid(μ) = √3∵ μ = Real Depth/Apparent Depth∴ Apparent Depth = Real Depth/μ∴ Apparent Depth = 9/√3∴ Apparent Depth = 9/√3 × √3/√3⇒ A.D. = 3√3 m.⇒ A.D. = 3 × 1.732⇒ A.D. = 5.196 m.Thus, the depth of the tank as seen by the man is 5.196 m.___________________Also,angle made by the line of sight with the Horizontal(or angle of Incidence) = 30°Now, μ =Sin i/Sin r⇒ √3 = Sin 30°/Sin r⇒ Sin r = 1/2 ÷ √3⇒ Sin r = √3/2⇒ Sin r = Sin 60°On Comparing, r = 60°Thus, angle of Refraction is 60°. RegardsAru. (askIITians forum expert)
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