I find money in the jar

A person looking into an empty container is able to see the far edge of the container’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 container’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.