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Question

A container has two layers of immiscible liquids 1 and 2 with refractive indices 1.5 and 4/3 respectively. What is apparent position of an object placed at the bottom of the vessel. Thickness of the layers are 3 cm and 8 cm respectively?


A
6 cm below the liquid 2 - air interface.
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B
8 cm below the liquid 2 - air interface.
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C
8 cm below the liquid 1 - liquid 2 interface.
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D
6 cm below the water - air interface.
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Solution

The correct option is B 8 cm below the liquid 2 - air interface.
Using Image shift in glass slab formula,
Shift of position of object due to liquids of refractive indices μ1,μ2 and thickness d1,d2 is
d1(11μ1)+d2(11μ2)
Here μ1=32,μ2=43 and thickness d1=3 cm,d2=8 cm
So shift = 3(123)+8(134)=3 cm upwards from bottom of the container.
Hence final position from air-liquid 2 interface is 8+33=8 cm below it

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