What is the Relationship Between the Mirror Equation and the Lens Equation?

[davidelete]

Homework Statement

Show that the mirror equation can be derived using the same principles that were used in deriving the equation for lenses.

Homework Equations

\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}

The Attempt at a Solution

There really doesn't appear to be any work to put into this. It just seems logical.

 

[davidelete]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

I am assuming the answer is 1.0 m + 0.3 m= 1.3 m.

 

[Delphi51]

Show that the mirror equation can be derived using the same principles that were used in deriving the equation for lenses.

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.

I am assuming the answer is 1.0 m + 0.3 m= 1.3 m.

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.

 

[davidelete]

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.

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

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.

Ah, so 1.6 m.

 

[Dadface]

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.

 

[davidelete]

It is a plane mirror.

 

[Delphi51]

Here is the lens law derivation: http://www.tutorvista.com/content/physics/physics-ii/light-refraction/convex-lens-formula.php

A convex or concave mirror has an equation very similar to the lens law, and it can be found using the same ray tracing technique. A plane mirror - not much to that!