question_answer

A beaker contains water up to a height \[{{h}_{1}}\]and kerosene of height \[{{h}_{2}}\] above water so that the total height of (water + kerosene) is \[({{h}_{1}}+{{h}_{2}}).\]Refractive index of water is \[{{\mu }_{1}}\] and that of kerosene is \[{{\mu }_{2}}.\] The apparent shift in the position of the bottom of the beaker when viewed from above is: [AIEEE 11-05-2011]

A) \[\left( 1+\frac{1}{{{\mu }_{1}}} \right){{h}_{1}}-\left( 1+\frac{1}{{{\mu }_{2}}} \right){{h}_{2}}\]

B) \[\left( 1-\frac{1}{{{\mu }_{1}}} \right){{h}_{1}}+\left( 1-\frac{1}{{{\mu }_{2}}} \right){{h}_{2}}\]

C) \[\left( 1+\frac{1}{{{\mu }_{1}}} \right){{h}_{2}}-\left( 1+\frac{1}{{{\mu }_{2}}} \right){{h}_{1}}\]

D) \[\left( 1-\frac{1}{{{\mu }_{1}}} \right){{h}_{2}}+\left( 1-\frac{1}{{{\mu }_{2}}} \right){{h}_{1}}\]

Correct Answer: B

Solution :

[b]

Apparent shift:

\[={{h}_{1}}\left( 1-\frac{1}{{{\mu }_{1}}} \right)+{{h}_{2}}\left( 1-\frac{1}{{{\mu }_{2}}} \right).\]