A student wants to find the refractive index of water by experiment. (a) Describe how the student could use a ruler and a search method to measure the appar...

(a) Method to measure apparent depth

1. Look directly down at the coin through the water from above. [1]
2. Hold a pin (or use a search method) above the water surface and adjust its height until it appears to be at the same depth as the image of the coin (no parallax between the pin and the image when the head is moved side-to-side). [1]
3. Measure the distance from the water surface down to the pin position; this is the apparent depth. [1]

(b) Refractive index of water

\(n = \frac{\text{real depth}}{\text{apparent depth}} = \frac{20.0}{15.0}\) [1]

\(n = 1.33\) [1]

This agrees with the accepted value for the refractive index of water.

(c) Assumption

The observer views from directly above (normal to the water surface), and the water surface is flat and undisturbed. [1] If viewed at an angle, refraction at the surface would distort the apparent position of the coin differently.

(d) Two improvements

1. Repeat the measurement several times and calculate the mean apparent depth to reduce random errors. [1]
2. Use a deeper container to increase both the real depth and the apparent depth, reducing the percentage uncertainty in the measurement. [1]

(e) Speed of light in water

The refractive index relates the speed of light in vacuum (or air) to the speed in the medium:

\(n = \frac{c}{v}\), so \(v = \frac{c}{n}\)

\(v = \frac{3.0 \times 10^8}{1.33}\) [1]

\(v = 2.26 \times 10^8\) m/s [1]

Light travels about 25% slower in water than in air, which is the physical reason for refraction at the water surface.