Question

You lay a mirror flat on the floor with one edge against a wall and aim a laser at the mirror. The ray reflects from the mirror and strikes the wall. The plane of the incident and reflected rays is perpendicular to the wall. The ray from the laser strikes the mirror 22.7 cm from the wall, and the reflected ray strikes the wall 35.5 cm above the mirror. Find the angle of incidence of the laser ray on the mirror.

Answer 1

Answer:

  About 32.6°

Explanation:

The tangent of the desired angle is the ratio of distance from the wall to height up the wall:

  tan(angle of incidence) = (22.7 cm)/(35.5 cm) ≈ 0.63944

  angle of incidence = arctan(0.63944) ≈ 32.6°

_____

The angle of incidence is measured from the normal to the mirror.

Answer 2

Answer:

32.6°

Explanation:

Thinking process:

The angle of incidence is measured from the normal. The normal is a perpendicular line that is imaginary.

Thus, the right angle approach is used:

We know that:

$tan\theta = \frac{opposite}{adjacent} \\tan (angle of incidence) = \frac{22.7}{35.5} \\\theta = tan^{-1}( \frac{22.7}{35.5})\\ = 32.6$

Thus, the angle is = 32.6°