Finding the Angle of Incidence in a Plane Mirror: Reflection of Light Homework

[TheHamburgler1]

Homework Statement

A person stands 3.6m in front of a wall that is covered floor to ceiling with a plane mirror. His eyes are 1.8m above the floor. He holds a flashlight between his feet and manages to point it at the mirror. At what angel of incidence must the light strike the mirror so the light will reach his eyes?

Homework Equations

angle of incidence=angle of reflection

The Attempt at a Solution

I don't know what equation to use to get the answer

 

[link2001]

Try drawing a picture of the problem. Diagrams are your best friend in optics problems.

 

[hage567]

Try drawing a picture of the problem. Diagrams are your best friend in optics problems.

Excellent advice, link2001!

Think trigonometry.

 

[nickthrop101]

yep, use trigonomety, draw a triangle, put x as the angle to the normal, the normal length is infinate but draw it as 3.6, and the height from the feet of the person , so that makes theta= inverse of tan( 0.9 divided by 3.6), that should give the angle to the normal. :D

 

[rwisz]

.

As a scientist, the first step in solving this problem would be to gather all the necessary information and identify any known equations or principles that can be applied. In this case, we have the distance between the person and the mirror (3.6m), the height of the person's eyes (1.8m), and the position of the flashlight between the person's feet. We also know that the angle of incidence is equal to the angle of reflection, according to the law of reflection.

To find the angle of incidence, we can use the following equation:

angle of incidence = arctan(height of person's eyes/distance between person and mirror)

Plugging in the values, we get:

angle of incidence = arctan(1.8m/3.6m) = 26.6 degrees

Therefore, the light must strike the mirror at an angle of 26.6 degrees in order to reach the person's eyes. This is because the angle of incidence is measured from the normal line (perpendicular to the mirror's surface) and the angle of reflection is measured from the same normal line, resulting in an angle of 53.2 degrees between the incident and reflected light rays. This angle is bisected by the mirror, resulting in an angle of 26.6 degrees between the incident light ray and the normal line.