Focal Length given M and distance between obj and img

In summary, the conversation is about finding the focal length of a lens based on the distance between an object and its upright image, as well as the magnification. Through the use of equations, it was determined that the distance for the image should be negative in order to produce a positive magnification, and by setting up a simultaneous equation, the focal length can be solved for.
  • #1
PhyHyped

Homework Statement


The distance between an object and its upright image is 28.0 cm. If the magnification is 0.550, what is the focal length of the lens that is being used to form the image?

Homework Equations


1/f = 1/so + 1/si
M= -si/so

The Attempt at a Solution


See included image.

Comments
I've been having a hard time with this all day any help would be amazing.

Can't seem to get the right answer.
 

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  • #2
Ok, there is one problem with your diagram. The image is on the wrong side of the lens. The object is a certain distance, s0, from the lens on the left side. The image is a certain distance, si, from the lens on the opposite side.

In your diagram, si + 0.28 m = s0. But you must remember that si is negative. Look back at your equation for magnification: m = -si/s0. The s0 is positive, so the distance for the image, si, should be negative in order to produce a positive magnification.

I hope that helped. Just try and do your same equations, but in the diagram, remember that the distance for the image in the equation is negative. Then, just list down all the equations you have, and you should see a simultaneous equation.
 
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Likes PhyHyped
  • #3
thanks! ill give that a try
 
  • #4
PhyHyped said:
thanks! ill give that a try
You're welcome.
 
  • #5
Solved it! Thanks again!
 

Related to Focal Length given M and distance between obj and img

1. What is the relationship between focal length, magnification, and the distance between the object and image?

The focal length is the distance between the lens and the image sensor when the subject is in focus. It is determined by the curvature of the lens and affects the magnification of the image. The magnification is the size of the image compared to the size of the actual object, and it increases as the focal length increases. The distance between the object and image also plays a role in determining the magnification, as it affects the size of the image projected onto the sensor.

2. How does changing the focal length affect the image?

Changing the focal length can have a significant impact on the image. A shorter focal length will result in a wider field of view, while a longer focal length will narrow the field of view. Additionally, a shorter focal length will result in a smaller image size, while a longer focal length will produce a larger image size. It is also important to note that changing the focal length can affect the depth of field and perspective of the image.

3. How do I calculate the focal length given the magnification and distance between the object and image?

The formula for calculating the focal length is: f = m x d, where f is the focal length, m is the magnification, and d is the distance between the object and image. Simply plug in the values for magnification and distance and solve for the focal length.

4. Can I change the focal length without physically changing the lens?

Yes, it is possible to change the focal length without physically changing the lens. This can be done through the use of zoom lenses, which allow you to adjust the focal length within a certain range. Some lenses also have a feature called "variable focal length" or "power zoom" that allows you to adjust the focal length electronically.

5. How does focal length affect the quality of the image?

The focal length does not directly affect the quality of the image. However, using a longer focal length can result in sharper images, as it reduces the effect of camera shake. Additionally, higher quality lenses tend to have longer focal lengths, so using a longer focal length can indirectly improve the quality of the image.

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