Question

An astronaut is exploring an unknown planet when she accidentally drops an oxygen canister into a 1.90-m-deep pool filled with an unknown liquid. Although she dropped the canister 46 cm from the edge, it appears to be 56 cm away when she peers in from the edge.

What is the liquid's index of refraction? Assume that the planet's atmosphere is similar to earth's.

Answer 1

Concepts and reason

The concepts used to solve this problem are the refractive index, incident angle, and the refracted angle.

Initially, use the depth of the pool and the distance of the dropped canister from the edge to calculate the angle of incidence and the angle of refraction.

Finally, use the relation between the incident angle and the refracted angle to calculate the refractive index.

Fundamentals

Expression for the refractive index is as follows:

Here, the refractive index is , angle of incidence is , and the angle of refraction is .

The diagram for the pool is as follows:

The tangent angle of incident ray is as follows:

Substitute for and for .

Solve for .

The tangent angle of the refracted ray is as follows:-

Substitute for and for .

Rearrange to get ,

Expression for the refractive index is as follows:

Substitute for and for .

Ans:

The refractive index of the liquid is