Optics and height of mirror problem

In summary, a man who is 160 cm tall and has his eyes 150 cm above the floor looks at his image in a plane mirror placed on a wall. In order to see his feet, the distance between the bottom edge of the mirror and the floor should be 75 cm. To see his image completely, the height of the mirror should be 80 cm. This can be determined by drawing a perpendicular line from the lower edge of the mirror to the line joining the foot and eye, and repeating the same for the line joining the top of the head and eye. The key to solving this problem is remembering that the angle between the incoming ray and the normal of the mirror is the same as the angle between the normal and the
  • #1
DanicaK
32
0

Homework Statement



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.

Homework 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 completely, what should the height of the mirror be?

The Attempt at a Solution

 
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  • #2


Hi, DanicaK, welcome to PF.
Can you draw the ray diagram. What is your attempt?
 
  • #3


Here it is.
 

Attachments

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  • #4


DanicaK said:
Here it is.
I can't see the picture.
 
  • #5


hm ... It's attachement and it is drown in Paint.
 
  • #6


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?

:)

[edit] also, the picture obviously worked for me too :)
 
  • #7


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


I know the things you said, but ...
 
  • #9


DanicaK said:
I know the things you said, but ...
Can you state the laws of reflection?
 
  • #10


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


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

But how to find them?
 
  • #12


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


I can't solve it yet.
 
  • #14


DanicaK said:
I can't solve it yet.
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


DanicaK said:
I can't solve it yet.

DanicaK said:
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.
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


O, OK :) Thanks a lot!
 

1. What is the relationship between optics and the height of a mirror?

The height of a mirror is directly related to its focal length, which is a measure of the mirror's ability to focus light. This relationship is known as the mirror equation: 1/f = 1/di + 1/do, where f is the focal length, di is the distance between the mirror and the image, and do is the distance between the mirror and the object.

2. How does the height of a mirror affect the image produced?

The height of a mirror determines the size of the image produced. A taller mirror will produce a larger image, while a shorter mirror will produce a smaller image. This is because the height of the mirror affects the angle at which light rays are reflected, which in turn affects the size and position of the image.

3. How can the height of a mirror be calculated?

The height of a mirror can be calculated using the mirror equation, as well as the magnification equation: M = -di/do = hi/ho, where M is the magnification, di is the distance between the mirror and the image, do is the distance between the mirror and the object, hi is the height of the image, and ho is the height of the object.

4. What is the difference between a concave and convex mirror in terms of height?

In a concave mirror, the height of the mirror is measured from the center of the mirror to the highest point on the curve, while in a convex mirror, the height is measured from the center to the lowest point on the curve. This is due to the different shapes of the mirrors, which affect the way light rays are reflected and the position of the image.

5. How does the height of a mirror affect its uses in optical devices?

The height of a mirror can determine its usefulness in different optical devices. For example, a taller mirror may be more useful for focusing light and producing larger images, while a shorter mirror may be better for reflecting light in a compact space. The height of a mirror can also affect the angle and direction of light rays, which is important for creating specific optical effects.

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