Question

Kyle lays a mirror flat on the floor and aims a laser at the mirror. The laser beam reflects off the mirror and strikes an adjacent wall. The plane of the incident and reflected beams is perpendicular to the wall. The beam from the laser strikes the mirror at a distance a=33.7 cm from the wall. The reflected beam strikes the wall at a height b=36.7 cm above the surface of the mirror. Find the angle of incidence θi at which the laser beam strikes the mirror.

Answer 1

Answer:

The angle of incidence is  $\theta_i =42.6^o$

Explanation:

The diagram for this question is shown on the first uploaded image

From the question we are told that

   The distance between the mirror and the wall is  $a = 33.7 cm$

    The height of the above the mirror is  $b = 36.7 cm$

Generally the angle which the reflected ray make with the mirror is mathematically evaluated as

             $\alpha =tan ^{-1} (\frac{b}{a})$

substituting values

             $\alpha = tan ^{-1}( \frac{36.7}{33.7})$

            $\alpha =47.4^o$

From the diagram we can deduce that  the angle of incidence is

             $\theta_i = 90 - \alpha$

So          $\theta_i = 90 - 47.4$

              $\theta_i =42.6^o$