# Optics and height of mirror problem

1. Sep 16, 2009

### DanicaK

1. The problem statement, all variables and given/known data

A man is 160 cm tall and hiss eyes are 150 cm above the floor. He looks at his image formed by a plane mirror pleaced on a wall.

2. Relevant equations

a) In order to see his feet, what should the distance beetwen the bottom edge of the mirror and the floor be?
b)To see his image completly, what should the height of the mirror be?

3. The attempt at a solution

2. Sep 16, 2009

### rl.bhat

Re: Optics

Hi, DanicaK, welcome to PF.
Can you draw the ray diagram. What is your attempt?

3. Sep 16, 2009

### DanicaK

Re: Optics

Here it is.

#### Attached Files:

• ###### untitled.bmp
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4. Sep 16, 2009

### rl.bhat

Re: Optics

I can't see the picture.

5. Sep 16, 2009

### DanicaK

Re: Optics

hm ... It's attachement and it is drown in Paint.

6. Sep 16, 2009

### essecks

Re: Optics

That diagram seems to have it.

Now just think about how you'd be able to figure out the height, and the measurements of that mirror?

:)

 also, the picture obviously worked for me too :)

7. Sep 16, 2009

### mgb_phys

Re: Optics

the diagram is correct, all you have to remember is that the angle between the incoming ray and the mirror ( actually the normal to the mirror ie. the horiontal) is the same as the reflected ray.

ps. Attachments take a few minutes to show up - they are checked by the staff to make sure they aren't spam/porn.

8. Sep 16, 2009

### DanicaK

Re: Optics

I know the things you said, but ...

9. Sep 16, 2009

### rl.bhat

Re: Optics

Can you state the laws of reflection?

10. Sep 16, 2009

### DanicaK

Re: Optics

The angle between the incoming ray and the normal of the mirror is the same as the angle between the normal and the reflected ray.

11. Sep 16, 2009

### DanicaK

Re: Optics

The solutions are:
a) 75 cm
b) 80 cm.

But how to find them?

12. Sep 16, 2009

### rl.bhat

Re: Optics

Draw a perpendicular from the lower edge of the mirror on the line joining foot of the person and his eye. It bisects the line. So what will be the distance between the lower edge of the mirror and the floor?
Repeat the same thing for the line joining the top of the head and eye.

13. Sep 16, 2009

### DanicaK

Re: Optics

I can't solve it yet.

14. Sep 16, 2009

### rl.bhat

Re: Optics

Distance between foot to eye is 150 cm.To see the foot, lower edge of the mirror should be at a height equal to half of this distance.

15. Sep 16, 2009

### essecks

Re: Optics

That is a key part of the solution. If the angles are the same, what does that say about the vertical distances (with regard to each other)?

16. Sep 17, 2009

### DanicaK

Re: Optics

O, OK :) Thanks a lot!