Refractive Index from Apparent Depth – Rankers Physics
Topic: Ray Optics
Subtopic: Refraction by Plane Surfaces

Refractive Index from Apparent Depth

If a container of height \(17.3\text{ cm}\) is filled with a liquid of refractive index \(\mu\). The bottom of container appear to be raised by \(3.46\text{ cm}\) when seen from above. Refractive index of liquid is
1.33
1.25
1.52
1.1

Solution:

The apparent shift is \(s = d\left(1 - \frac{1}{\mu}\right)\). Substituting the values: \(3.46 = 17.3 \left(1 - \frac{1}{\mu}\right) \implies 1 - \frac{1}{\mu} = 0.2 \implies \mu = 1.25\).

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