A physics class investigates an unknown transparent plate. A narrow laser beam in air is directed toward the plate at six different incident angles; the corresponding refracted angles inside the plate are measured and recorded in the table below.
Incident Angle θi (deg) 15 25 35 45 55 65
Refracted Angle θr (deg) 10 17 24 30 36 41
(a) Complete a data table that adds two new columns: sinθi and sinθr for each trial. Use at least three significant figures.
(b) On graph paper, sketch a graph of sinθi (vertical axis) versus sinθr (horizontal axis). Your sketch should clearly label axes, include a best-fit straight line, and indicate the slope.
(c) From the slope of your line, obtain a value for the index of refraction of the plate. Show all reasoning that connects the slope to the index.
(d) Standard reference values for common materials are: acrylic 1.49; borosilicate glass 1.47; polycarbonate 1.58. Identify the most probable material and calculate the percent difference between your experimental value and the accepted value.
(e) One student claims that systematic error is present because the laser beam widens slightly after passing through the plate. Discuss qualitatively how this effect could influence the slope of the graph and, consequently, the calculated index.