Physics

Problem

A tank contains water to a depth of

6\,\text{cm}

and its surface is covered by a plane glass plate

1\,\text{cm}

thick. The refractive indices of water and glass are

1.33

and

1.5

respectively. For an observer looking normally from air, what is the apparent depth of the object at the tank bottom measured from the top surface of the glass? a)

4.75\,\text{cm}

5.18\,\text{cm}

4.51\,\text{cm}

5.51\,\text{cm}

Intuitive explanation

The key is understanding that light bends when crossing boundaries between different materials, making objects appear closer than they actually are. You'll need to track how the apparent depth changes as light passes through each layer—glass then water—by applying the refraction formula $n_1 d_1 = n_2 d_2$ at each interface. Work backwards from the tank bottom through each medium, accounting for how the refractive index of each layer compresses the apparent distance.

Intuitive explanation

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