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

Click For Summary
SUMMARY

The problem involves calculating the angle at which a vertical mirror must be tilted to allow a person standing 1.80 m away to see their eyes reflected. The observer's eye level is 1.95 m above their feet, and the angle of incidence equals the angle of reflection. Initial calculations suggest that the angles for viewing the shoes are approximately 62 degrees. To determine the angle for viewing the eyes, the observer must set up a second triangle using the known distance and apply trigonometric principles to find the required angle of tilt for the mirror.

PREREQUISITES
  • Understanding of basic trigonometry, specifically right triangles
  • Knowledge of the law of reflection (angle of incidence equals angle of reflection)
  • Familiarity with geometric principles related to angles and distances
  • Ability to visualize and manipulate geometric figures
NEXT STEPS
  • Study the properties of isosceles triangles in relation to angles of incidence and reflection
  • Learn how to apply trigonometric functions to solve for unknown angles in right triangles
  • Explore the concept of similar triangles to simplify reflection problems
  • Practice problems involving mirrors and angles to reinforce understanding of reflection principles
USEFUL FOR

Students studying physics, particularly those focusing on optics, geometry enthusiasts, and anyone interested in practical applications of trigonometry in real-world scenarios.

map7s
Messages
145
Reaction score
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.
 
Physics news on Phys.org
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
 
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?
 

Similar threads

Multiple reflections in a mirror system
  • · Replies 5 ·
Replies
5
Views
508
Mirror system in geometrical optics
  • · Replies 9 ·
Replies
9
Views
2K
What Is the Angle of Reflection in a Plane Mirror?
  • · Replies 11 ·
Replies
11
Views
2K
Light rays reflected off vertical mirror (law of reflection)
  • · Replies 12 ·
Replies
12
Views
2K
Total Internal Reflection and Transmitted Wavelength
  • · Replies 1 ·
Replies
1
Views
948
How does the surface of a refracting prism become reflective?
  • · Replies 2 ·
Replies
2
Views
1K
Finding the distance of reflection in a mirror
  • · Replies 19 ·
Replies
19
Views
4K
Angle of Deflection of Laser Given Tilted Mirror
  • · Replies 10 ·
Replies
10
Views
5K
How to solve for angle of reflection in respect to floor?
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Mirror rotates any polarisation by 90°?
  • · Replies 6 ·
Replies
6
Views
4K