An optical engineer is investigating the refractive properties of a newly developed high-index polymer, Hydra-gel, designed for advanced contact lenses.
To determine the refractive index of the polymer, she shines a green laser beam through a semi-cylindrical sample of the polymer at various angles of incidence, iii, and measures the corresponding angles of refraction, rrr.
Her experimental results are recorded in the table below:
| Angle of incidence, iii | Angle of refraction, rrr | sini\sin isini | sinr\sin rsinr |
|---|---|---|---|
| 15∘15^\circ15∘ | 9∘9^\circ9∘ | 0.26 | 0.16 |
| 30∘30^\circ30∘ | 18∘18^\circ18∘ | 0.50 | [P] |
| 45∘45^\circ45∘ | 26∘26^\circ26∘ | 0.71 | [Q] |
| 60∘60^\circ60∘ | 33∘33^\circ33∘ | 0.87 | 0.54 |
| 75∘75^\circ75∘ | 37∘37^\circ37∘ | 0.97 | 0.60 |
Calculate the missing values [P] and [Q] of sinr\sin rsinr from the table, giving your answers to 2 decimal places.
The engineer plots a graph of sini\sin isini on the yyy-axis against sinr\sin rsinr on the xxx-axis. The straight line of best fit passes through the origin (0.00,0.00)(0.00, 0.00)(0.00,0.00) and the coordinate point (0.45,0.72)(0.45, 0.72)(0.45,0.72). Use these values to calculate the refractive index of the Hydra-gel polymer.
Suggest two reasons why finding the refractive index using a graphical method is superior to calculating it directly from a single pair of angles in the table.
