A small mirror is attached to a vertical wall at a distance of 1.50 meters above

Question

A small mirror is attached to a vertical wall at a distance of 1.50 meters above the floor. The mirror faces East toward a wall of openings at an archaeological site at the equator thought to be used for timekeeping. On the day of the equinox at 8:00 AM, a reflected ray from the mirror strikes the floor at a distance of 4.21 meters from the base of the wall, where there is a specific marking in the floor. Later in the morning, light passes through a different opening, then reflects off the mirror to strike the floor at a marking 1.28 m from the wall.

You can assume the sun’s path is vertical, and it moves 15.0° per hour due to the rotation of the Earth, and you can assume the rays in question lie in a plane that is perpendicular to both the wall and the floor. Approximately what time of the morning does a sun ray from the mirror strike the mark on the floor that is 1.28 m from the wall?

Explanation / Answer

let Alpha(A) , Beta(B) and gamma (G) be the angles

here B is the aggle formed by the mirror and incident or reflected rays

G be the angle of relfected rays during day time

A be angle rotated by earth

tan B = 1.28/1.5  

B = 40.47 deg

tan G = 4.21/1.5

G = 70.38 deg

A = G-B

A = 70.38 - 40.47

A = 29.91 deg

time interval = 29.91*1h/15

t = 2 hrs

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