A small mirror is attached to a vertical wall, and it hangs a distance of 1.97 m

Question

A small mirror is attached to a vertical wall, and it hangs a distance of 1.97 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 3.12 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.13 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?

Explanation / Answer

let the angle of incidence (or reflection) for the two rays be i1 and i2.

hence, by trigonometry,

h cot i1 = 3.12      and     h cot i2 = 1.13 , where h = 1.97

hence we get i1 = 32.27 deg and i2 = 60.16 deg.

hence the rotation of earth is i1-i2 = 27.89 deg.

time elapsed = 27.89 / 15 hrs = 1.85 hrs

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