A small mirror is attached to a vertical wall, and it hangs a distance of 1.82 m

Question

A small mirror is attached to a vertical wall, and it hangs a distance of 1.82 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 3.89 m from the base of the wall. Later on in the morning, the ray is observed to strike the floor at a distance of 1.18 m from the wall. The earth rotates at a rate of 15.0

Explanation / Answer

use snel decartes law

tan(theta1)=y/x1

=1.82/3.89

=0.467

theta1=tan inverse of(0.467)

=25.03degrees

tan(theta2)=y/x2

=1.82/1.18

=1.542

theta1=tan inverse of(1.542)

=57.03degrees

as sun rises change in angle=57.03-25.03

=32degrees

elapsed time=32*1/15

=2.13hours

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