Location of object on axis of concave mirror?

In summary, to get a half-size image with a concave mirror, the object should be placed at a distance of 2f from the mirror's vertex, following the sign convention. This can be determined by using the equation (H'/H)=(f/k) where H' and H are the heights of the image and object respectively, and f is the focal length of the mirror. A diagram may be helpful in understanding the relationship between the image and object distances.
  • #1
jlmccart03
175
9

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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  • #2
Those equations don'tmention image size. So you need an idea about that, or maybe an equation.
Have you drawn a diagram?
 
  • #3
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)
 
  • #4
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.)
 
  • #5
concave_mirror.png
 
Last edited:

Related to Location of object on axis of concave mirror?

1. What is the axis of a concave mirror?

The axis of a concave mirror is an imaginary line that passes through the center of the mirror and is perpendicular to its surface. It is used as a reference point for measuring the positions of objects and images formed by the mirror.

2. How is the location of an object determined on the axis of a concave mirror?

The location of an object on the axis of a concave mirror is determined by measuring the distance of the object from the center of the mirror. This distance is known as the object distance and is denoted by the letter "u".

3. What is the significance of the object location on the axis of a concave mirror?

The object location on the axis of a concave mirror is important because it affects the position and characteristics of the image formed by the mirror. The closer the object is to the mirror, the larger the image will be and the farther the object is, the smaller the image will be.

4. Can the location of an object on the axis of a concave mirror be negative?

Yes, the location of an object on the axis of a concave mirror can be negative. This occurs when the object is located behind the center of the mirror, meaning the object distance "u" is less than 0. This results in a virtual image being formed by the mirror.

5. How does the location of the object on the axis of a concave mirror affect the image distance?

The location of the object on the axis of a concave mirror directly affects the image distance, which is the distance between the mirror and the image formed. As the object distance increases, the image distance decreases and vice versa. This relationship is represented by the formula: 1/f = 1/u + 1/v, where "f" is the focal length of the mirror and "v" is the image distance.

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