Question

Ch 25 Q 8 Go.) Problem A small mirror is attached to a vertical wall, and it hangs a distance of 1.86 m above the floor. The mirror is facing due east, and a ray of sunlight strikes the mirror early in the morning and then again later in the morning. The incident and reflected rays lie in a plane that is perpendicular to both the wall and the floor. Early in the morning, the reflected ray strikes the floor at a distance of 3.14 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.40 m from the wall. The earth rotates at a rate of 15.0˚ per hour. How much time (in hours) has elapsed between the two observations?

Answer 1

Assume that particular ray reflects from the very bottom of the mirror.
Angle of the reflection in morn = arctan (1.86/3.14) =30.6406634 degrees.

Angle of reflection later = arctan (1.86/1.40) =53.031656degrees.
Change in angle = (53.031656-30.6406634) = 22.3099degrees.
(22.309926/15) = 1.49hrs.