A person looking into an empty container is able to see the far edge of the containerâ€™s bottom. The height of the container is \(h\), and its width is \(d\). When the container is completely filled with a fluid of index of refraction \(n\) and viewed from the same angle, the person can see the center of a coin at the middle of the containerâ€™s bottom.

Question is that if the the container has a width of \(8 \,\text{cm}\) and is filled with water, then find the height of the container in \(\text{cm}\) to 2 decimal places.

**Details and assumptions**

- The refractive index, \(n\) for water is \(\dfrac{4}{3}\).
- Use calculator if required.

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