A student conducts an experiment using a semicircular polymer block to investigate the refraction of light.
List three other pieces of equipment (excluding the polymer block and a light source/ray box) that the student needs to record the paths of the light rays and measure the angles of incidence and refraction.
The student shines a ray of light from air towards the midpoint P P\,P of the flat face of the semicircular block. (i) Explain why the ray of light changes direction as it enters the block at PPP. (ii) Describe how the speed and wavelength of the light wave change when it enters the polymer block.
The student varies the angle of incidence i i\,i in air and measures the corresponding angle of refraction r r\,r inside the block, obtaining the following results:
| Angle of incidence, iii | Angle of refraction, rrr | sini\sin isini | sinr\sin rsinr |
|---|---|---|---|
| 15∘15^\circ15∘ | 10∘10^\circ10∘ | 0.26 | 0.17 |
| 30∘30^\circ30∘ | 20∘20^\circ20∘ | 0.50 | 0.34 |
| 45∘45^\circ45∘ | 28∘28^\circ28∘ | 0.71 | 0.47 |
| 60∘60^\circ60∘ | 36∘36^\circ36∘ | 0.87 | 0.59 |
| 75∘75^\circ75∘ | 40∘40^\circ40∘ | 0.97 | 0.64 |
(i) State the mathematical relationship between the refractive index nnn, the angle of incidence iii, and the angle of refraction rrr. (ii) If a graph of sini\sin isini (on the vertical axis) against sinr\sin rsinr (on the horizontal axis) is plotted, explain how the gradient of the line of best fit represents the refractive index nnn. (iii) Use the data in the table to calculate the refractive index n n\,n of the polymer.
