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A jar of height h is filled with a transparent liquid of refractive index mu(See figure). At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmertically aobut the centre , the dot is invisible |
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Answer» Solution :`rArr` Suppose required minimum DIAMETER of given disc is d. Here for the light rays emanating from point like object O and then becoming incident on water surface (from inside), if `i gt C,` then that object O wil not be see by the observer while observing from outside the water. (Where C = critical angle for water to air) Suppose angle i in the figure is equal to C . Now, according to formula. `sin C = 1/mu` `THEREFORE sin i = 1/mu( because C = i)` From the figure, `tan i=(d/2)/(h)` `therefore d/2 = h tan i ......(1)` Now, sin ` i = 1/mu` `thereforecos i = SQRT(1 sin ^2i) = sqrt(1 - 1/(mu^2)) = (sqrt(mu^2 -1))/(mu)` `therefore tan i = (sin i)/(cos i) = (1/u)/(sqrt(mu^2-1)/(mu))=(1)/(sqrt(mu^2-))` `therefore` From equation (1), `d/2 = h xx (1)/(sqrt(mu^2 - 1))` `therefore d = (2h)/(sqrt(mu^2-1))` Above equation GIVES required result. |
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