Height of Mirror Needed to See Table in Mirror

Click For Summary

Homework Help Overview

The problem involves determining the minimum height of a plane mirror needed for a person to see the top of a table in the mirror. The person is 1.9 m tall and stands 3.5 m away from the mirror, while the table is 0.80 m high and located 1.5 m in front of the mirror.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the height of the mirror and the height of the person and the table. There is mention of using similar triangles to establish proportional relationships. One participant attempts to apply knowledge about mirror height requirements based on their own height.

Discussion Status

Some participants have offered hints about using ray diagrams and similar triangles to approach the problem. There is an indication that one participant has attempted a calculation but received feedback that their answer was incorrect. The discussion reflects a mix of attempts and clarifications without a clear consensus on the correct approach yet.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is a focus on understanding the geometric relationships involved in the problem.

matt72lsu
Messages
94
Reaction score
0

Homework Statement


You are 1.9 m tall and stand 3.5 m from a plane mirror that extends vertically upward from the floor. On the floor 1.5 m in front of the mirror is a small table, 0.80 m high.

a) What is the minimum height the mirror must have for you to be able to see the top of the table in the mirror?


Homework Equations



pythag. theorem?

The Attempt at a Solution


i know the mirror has to be half as tall as the person in order to see their body but I'm not sure how to use this knowledge to translate it to the table. thanks for your help!
 
Physics news on Phys.org
Can you draw the ray diagram?
Let h be the height of the table and H be the minimum height of the mirror from the ground.
A ray from the top of the table T falls on the mirror at M and reflects towards your eye E. Draw two parallel lines from T and M to the ground. Parallel line from T meets the mirror at N and parallel line from M meets you at P.
Now you can varify easily that the triangles EPM and TNM are similar. So the sides of the triangles are proportional. With these hints try to find the minimum height of the mirror.
 
i got like 1.2m but it said it was wrong.
 
The formula becomes
(H - 0.8)/1.5 = (1.9 - H)/3.5)
Solve for H.
 
thanks! i was close lol
 

Similar threads

Replies
3
Views
5K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 2 ·
Replies
2
Views
7K
Replies
1
Views
6K
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 15 ·
Replies
15
Views
3K
  • · Replies 1 ·
Replies
1
Views
10K