Image Distance and Magnification

In summary, the conversation discusses the position and magnification of an image formed by a convex mirror. The object is located 23.4 cm from the center of a silvered spherical glass Christmas tree ornament with a diameter of 5.70 cm. The position of the image is calculated to be -1.12 cm and the magnification is 0.048. However, there is a mistake in the calculation and it is suggested to redo it.
  • #1
erik-the-red
89
1
Question

An object is a distance of 23.4 cm from the center of a silvered spherical glass Christmas tree ornament which has a diameter of 5.70 cm.

A What is the position of its image?

B What is the magnification of its image?

I think the object can be treated as a convex mirror.

s (object distance) = 23.4 cm
R = -(5.70)/2 = -2.85 cm

[tex]\frac{1}{s} + \frac{1}{s'} = \frac{2}{R}[/tex]

Using that equation, I get [tex]\frac{1}{s'} = \frac{2}{-2.85} - \frac{1}{23.4}[/tex].

Then, s' = -1.12 cm.

And, [tex]m = -\frac{s'}{s}[/tex], so m = .048.

I know for sure that -1.12 cm is not the correct answer, so most likely my second answer is also incorrect.

What did I do wrong?
 
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  • #2
Did I not provide enough work?
 
  • #3
Your method is fine but check your arithmetic.
 
  • #4
Sorry, I still get the same answer.
 
  • #5
erik-the-red said:
Using that equation, I get [tex]\frac{1}{s'} = \frac{2}{-2.85} - \frac{1}{23.4}[/tex].

Then, s' = -1.12 cm.
Please redo this calculation.
 
  • #6
Doc Al,

Indeed, it was incorrect. Thanks!
 

1. What is image distance?

Image distance refers to the distance between the object and the image formed by a lens or mirror. It is measured from the lens or mirror to the location of the image.

2. How is image distance related to object distance?

Image distance and object distance are inversely related. This means that as the object distance increases, the image distance decreases and vice versa.

3. What is magnification?

Magnification is the ratio of the size of the image to the size of the object. It can be either positive or negative, indicating whether the image is upright or inverted.

4. How is magnification calculated?

Magnification is calculated by dividing the image distance by the object distance. The resulting number can be used to determine the size and orientation of the image.

5. Can image distance and magnification be changed?

Yes, the image distance and magnification can be changed by altering the object distance or by adjusting the focal length of the lens or mirror. The type of lens or mirror used can also affect these values.

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