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A microscope is focused on an object resting at the bottom of a container. A liquid of refractive index 5/3 is then poured into the container. The microscope must be raised by 8 cm to bring the object back into focus. Find the height of the liquid in the container (in cm).

1. 10
2. 15
3. 20
4. 25

Correct answer: 20

Solution

When liquid of refractive index n = 5/3 fills to height h, the apparent depth of the liquid layer is h/n = 3h/5. The microscope must be raised by h - 3h/5 = 2h/5. Setting 2h/5 = 8 gives h = 20 cm.

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