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

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Homework Help Overview

The discussion revolves around the relationship between the mirror equation and the lens equation, exploring the principles used in their derivations. Participants are examining specific scenarios involving mirrors and the implications of object and image distances.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the derivation of the mirror equation using principles similar to those for lenses, questioning the specific principles used in the lens equation derivation. There are attempts to clarify the distances involved in a practical scenario with mirrors.

Discussion Status

The discussion is active, with participants sharing their thoughts on the derivation process and the nature of the mirrors involved. Some guidance has been offered regarding the use of ray tracing techniques, and there is an exploration of different types of mirrors.

Contextual Notes

Participants are considering the implications of using different types of mirrors, such as plane, concave, and convex mirrors, and how these affect the relationships between object and image distances. There is also mention of assumptions regarding the nature of the mirrors being discussed.

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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.
 
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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.
 
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.
 
Delphi51 said:
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.
 
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.
 
It is a plane mirror.
 
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!
 

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