# Mirror and lens equations

1. Feb 1, 2009

### davidelete

1. The problem statement, all variables and given/known data
Show that the mirror equation can be derived using the same principles that were used in deriving the equation for lenses.

2. Relevant equations
$$\frac{1}{f}$$=$$\frac{1}{d_{o}}$$+$$\frac{1}{d_{i}}$$

3. The attempt at a solution
There really doesn't appear to be any work to put into this. It just seems logical.

2. Feb 1, 2009

### davidelete

1. The problem statement, all variables and given/known data
A woman with a bow in the back of her hair is looking into a dresser mirror 1.0 meter away. She is holding a mirror 0.3 m behind her head so that she can see the bown in the dresser mirror. How far behind the dresser mirror is the image of the bow?

2. Relevant equations

3. The attempt at a solution
I am assuming the answer is 1.0 m + 0.3 m= 1.3 m.

3. Feb 1, 2009

### Delphi51

What principles did your textbook use in deriving the lens equation?
Do you recall drawing some rays from object to image through the lens? I think there are 3 special rays that are easy to draw, and a bit of work with similar triangles gives you that formula.

She would see herself 1 m behind the mirror and the frame of the small mirror will be seen 1.3 m behind. But the image of the bow will be further yet.

4. Feb 1, 2009

### davidelete

I am looking, not seeing too much in the way of any good diagrams.

Ah, so 1.6 m.

5. Feb 1, 2009

Is it a plane mirror ,a concave mirror or a convex mirror?For curved mirrors use geometry as suggested by Delphi51- if it is a plane mirror f is infinite..1/f is zero and therefore
1/do=-1/d1,in other words the object distance equals the image distance.The minus sign shows that for a real object the image is virtual.

6. Feb 1, 2009

### davidelete

It is a plane mirror.

7. Feb 1, 2009