How can I calculate the angle of a tilted mirror to see my reflection?

In summary, the problem involves finding the angle at which a mirror should be tilted for a person standing at a certain distance to see their own eyes reflected in the mirror. The angle of incidence is equal to the angle of refraction, and the person's height and the distance to the mirror are known. The first attempt to solve the problem involved creating right triangles and finding the angles of incidence and refraction, but it was unclear how to proceed from there. The solution involves setting up a second triangle with the angle of the mirror as the unknown and using the known distance to solve for the angle.
  • #1
map7s
146
0

Homework Statement



You stand 1.80 m in front of a wall and gaze downward at a small vertical mirror mounted on it. In this mirror you can see the reflection of your shoes. If your eyes are 1.95 m above your feet, through what angle should the mirror be tilted for you to see your eyes reflected in the mirror? (The location of the mirror remains the same, only its angle to the vertical is changed.)


I know that the angle of incidence is equal to the angle of refraction and I tried creating triangles to solve this problem. For the first case, where you can see your shoes, when I drew the triangle, it was isoceles, so I split it up into to equal right triangles and found that the angles of incidence and refraction were about 62 degrees, but I did not know where to go from there or if I was even on the right track.
 
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  • #2
thats pretty much the whole problem. now that you know what angle the mirror is set at, figure out what angle the mirror should be set at to see your eyes and subtract
 
  • #3
that was just what I was wondering - how can I set up that second triangle with the angle of the mirror? I only know the value of one side (the distance), so how can I solve for the angle?
 

What is reflection?

Reflection is the phenomenon of bouncing back of light or other waves from a surface when it encounters that surface.

How do mirrors reflect light?

Mirrors are made of a smooth and highly polished surface, which allows light to bounce off of it at the same angle it hits the surface. This results in a clear and accurate reflection of the original image or object.

What is the difference between specular and diffuse reflection?

Specular reflection occurs when light reflects off of a smooth and shiny surface, like a mirror, at a definite angle. Diffuse reflection occurs when light reflects off of a rough surface and is scattered in different directions.

How does the shape of a mirror affect reflection?

The shape of a mirror can affect reflection in two ways. First, the curvature of the mirror can determine the type of reflection (concave or convex). Second, the shape can also affect the size and orientation of the reflected image.

Can reflection occur with non-visible light?

Yes, reflection can occur with all types of electromagnetic radiation, not just visible light. This includes radio waves, microwaves, infrared, ultraviolet, x-rays, and gamma rays. The only difference is that we cannot see the reflection of these types of radiation with our eyes.

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