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A beaker contains water up to a height h...

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 :-

A

`(1+(1)/(mu_(1)))h_(1)-(1+(1)/(mu_(2)))h_(2)`

B

`(1+(1)/(mu_(1)))h_(1)+(1-(1)/(mu_(2)))h_(2)`

C

`(1+(1)/(mu_(1)))h_(2)-(1+(1)/(mu_(2)))h_(1)`

D

`(1-(1)/(mu_(1)))h_(2)+(1-(1)/(mu_(2)))h_(1)`

Text Solution

Verified by Experts

The correct Answer is:
B

Actual depth `=(h_(1)+h_(2))`
Shift of bottom due to water
`d_(1)=h_(1)-(h_(1))/(mu_(1)))`
`=(1-(1)/(mu_(1))h_(1)`
Shift of bottom due to kerosene
`d_(2)=(h_(2)-(h_(2))/(mu_(2)))=h_(2)(1-(1)/(mu_(2)))`
Combined shift of bottom when viewed from above
Total shift `=d_(1)+d_(2)`
Apparent shift in the position
`h_(2)=(1-(1)/(mu_(1)))+h_(2)(1-(1)/(mu_(2)))`
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Knowledge Check

  • A vesse of depth x is half filled with oil of refractive index mu_(1) and the other half is filled with water of refrative index mu_(2) . The apparent depth of the vessel when viewed above is

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  • A beaker is filled with two immiscible transparent liquids of refractive indices mu_1 and mu_2 having thickness of layers d_1 and d_2 respectively. The apparent depth of the bottom of the beaker is

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