Location of object on axis of concave mirror?

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Homework Help Overview

The discussion revolves around determining the object distance for a concave mirror to achieve a half-size image, expressed in terms of the focal length. The problem involves understanding the relationships between object distance, image distance, and image size within the context of mirror equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of mirror equations and question their applicability to the problem of image size. There is an exploration of the relationship between object distance and image size, with suggestions to consider diagrams for clarity.

Discussion Status

The discussion is ongoing, with participants offering insights into the relevant equations and questioning the original poster's approach. Some guidance has been provided regarding the importance of understanding the ratio of heights and its connection to distances, but no consensus has been reached on the correct method to solve the problem.

Contextual Notes

There is a mention of the need to follow the sign convention and the potential confusion regarding the formulas used. Participants are also considering the implications of the image size in relation to the object distance.

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Homework Statement


Where on the axis of a concave mirror would you place an object to get a half-size image? Express the object distance in terms of the focal length f. Follow the sign convention.

Homework Equations


(1/q)+(1/p)=(1/f)
f=(2/R)

The Attempt at a Solution


I attempted to use the object distance plus image distance to solve for f (I just got f=q+p), but the online homework system says that is wrong. Are these the correct formulas and what should I be doing?
 
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Those equations don'tmention image size. So you need an idea about that, or maybe an equation.
Have you drawn a diagram?
 
Merlin3189 said:
Those equations don'tmention image size. So you need an idea about that, or maybe an equation.
Have you drawn a diagram?
But they do? I wrote them differently, but it's (1/Do)+(1/Di)=(1/f)

EDIT: wait I misread that. You are talking about (H'/H)=(f/k)
 
Yes. I don't recognise the formula you give (H'/H)=(f/k) ?
But it's the ratio of heights (H'/H) that matters. You know what number this is, from the question.
How do the heights relate to the distances ? (That's where I thought a diagram might help.)
 
concave_mirror.png
 
Last edited:

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