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There is a cylindrical vessel of radius 10 cm and a cylindrical glass piece of radius 5 cm and height 10 cm is kept inside it. Volume of water 950 pi cm^(3) is poured into it. Bottom of the glass piece is seen with paraxial rays. What will be the apparent depth of bottom of glass cylinder? Index of refraction of glass is 3//2 and that of water is 4//3. |
Answer» Solution :Let h be the total height of the water from bottom as shown in figure.  `"Total VOLUME of water"=950 pi cm^(3)` `pi(10)^(2)h-pi(5)^(2)xx10=950pi` `rArr""100pih-250pi=950pi` `rArr""h=12cm` Height of layer of water above the cylindrical glass piece is `=12-10=2cm`. We can use the following relation to CALCULATE apparent DEPTH : `"apparent depth"=("REAL depth")/(MU)` Apparent depth of the bottom of glass piece `=(2)/(4//3)+(10)/(3//2)=(3)/(2)+(20)/(3)=(9+40)/(6)=(49)/(6)cm`. |
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