A student is practicing drawing ray diagrams for a flat bathroom mirror mounted vertically on a wall. In her notebook she sketches a single incident ray that meets the mirror surface at a point P. She labels the angle between the incident ray and the mirror surface as 35∘ and then draws what she believes is the normal, but her “normal” is NOT perpendicular to the mirror surface.
Answer the following about the quality of the student’s construction and how to correct it.
(a) State the geometrical relationship that must always exist between the angle made by an incident light ray with the normal and the angle made by the reflected ray with the normal at point P.
(b) Using the numerical value written by the student, calculate the correct value (in degrees) that should appear as the angle between the reflected ray and the mirror surface.
(c) Explain qualitatively how drawing a normal that is not perpendicular to the mirror surface will change the predicted direction of the reflected ray. In your explanation, specify whether the reflected ray will be drawn too far upward, too far downward, or simply at the wrong angle altogether.
(d) Describe, in a step-by-step manner suitable for use with a ruler and a protractor, how the student should redraw the normal and the reflected ray so that the construction satisfies the requirement identified in part (a).