How long is the image of the meter stick?

The image of the first end is at 120 cm and the image of the second end is at 53.3 cm. Therefore, in summary, the image of the meter stick in the concave mirror is 66.7 cm long.
  • #1
rayhan619
77
0

Homework Statement



The figure shows a meter stick held lengthwise along the optical axis of a concave mirror. (Intro 1 figure) - figure attached

How long is the image of the meter stick?

Homework Equations



1/f = 1/do + 1/di

3. The Attempt at a Solution [/b

1/di = 1/f - 1/do = 1/40 -1/60
di = 120 cm

but I am not sure how to proceed after this part

any help would be appreciated
 

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  • #2
You found the location of the image of one end of the stick; now find the other.
 
  • #3
so for the second point
1/di = 1/f - 1/do = 1/40 - 1/160
di = 53.3

so the length of the scale would be (120+53.3) = 173.3 cm

or (120-53.3) = 66.7 cm ?
 
  • #4
The length of the image will be the difference in the position of each end.
 

Related to How long is the image of the meter stick?

1. How is the length of an image of a meter stick determined?

The length of an image of a meter stick is determined by the magnification of the lens or mirror used to create the image. It is a proportional relationship, where the length of the image is equal to the length of the object multiplied by the magnification factor. For example, if the magnification is 2x, the image of a meter stick will appear to be 2 meters long.

2. Does the distance between the object and the lens/mirror affect the length of the image?

Yes, the distance between the object and the lens/mirror does affect the length of the image. This is because the magnification factor is also influenced by the distance between the object and the lens/mirror. The farther the object is from the lens/mirror, the smaller the magnification and therefore the shorter the image will appear.

3. How does the focal length of the lens/mirror impact the length of the image?

The focal length of the lens/mirror is the distance from the lens/mirror to the point where the image is in focus. The longer the focal length, the smaller the magnification and therefore the shorter the image will appear. Conversely, a shorter focal length will result in a larger magnification and a longer image.

4. Can the length of an image of a meter stick be greater than 1 meter?

Yes, the length of an image of a meter stick can be greater than 1 meter. This is possible with the use of a convex lens or concave mirror, which have a magnification factor greater than 1x. However, the magnification factor cannot exceed the maximum focal length of the lens/mirror.

5. Is the length of an image of a meter stick affected by the wavelength of light?

No, the length of an image of a meter stick is not affected by the wavelength of light. The length of the image is solely dependent on the magnification factor, which is determined by the lens/mirror and the distance between the object and the lens/mirror. The wavelength of light does not play a role in this relationship.

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