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A small air bubble in glass shpere of radius `2 cm` appears to be `1 cm` from the surface when looked at, along a diameter. If the refractive index of glass is `1.5`, find the true position of the air bubble. |
Answer» Correct Answer - `1.2 cm` Here, `mu_(1), mu_(2) = 1.5, R = - 2cm` Incident ray `OA` in glass is refracted in air, along `AB`, and appears to some from `I`. `u = PO = ? v = PI = - 1 cm` As refraction occurs from denser to rarer medium, `:. -(mu_(2))/(u) + (mu_(1))/(v) = (mu_(1) - mu_(2))/(R )` `-(1.5)/(u) + (1)/(-1) = (1 - 1.5)/(-2) = (1)/(4)` `(1.5)/(u) = -1 - (1)/(4) = -(5)/(4)` `u = (-4 xx 1.5)/(5) = - 1.2 cm` The air bubble `O` lies at `1.2 cm` from the refracting surface within the sphere. |
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