Finding focal length given magnification and object distance?

In summary, to find the focal length of the lens being used to form the image, we can use the equations p+q=15.5 and -q/p=0.7. These equations can be derived from the properties of a concave/diverging lens, which produces a diminished, upright image that is virtual and located on the same side of the lens as the object. By solving for the values of p and q, we can determine that the focal length is 22.1 cm.
  • #1
speedrsr
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The distance between an object and its upright image is 15.5 cm. If the magnification is 0.7, what is the focal length of the lens being used to form the image?

Answer in units of cm.

So I tried combining the equations p+q=15.5 and -q/p=.7 and still was unable to come up with a correct answer.. How exactly do can you find the focal length with only the magnifaction and distance?
 
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  • #2
For there to be a diminished, upright image we are looking at a concave/diverging lens.
The virtual image is on the same side of the lens as the object. It is also nearer the lens. This can be shown on a ray diagram.
This gives q/p =0.7 and p-q = 15.5
Solve for p and q
 

1. What is the formula for finding focal length given magnification and object distance?

The formula for finding focal length is f = m * d, where f represents focal length, m represents magnification, and d represents object distance.

2. How do I determine the magnification and object distance in order to find focal length?

Magnification can be determined by dividing the image distance by the object distance, while object distance is the distance between the object and the lens. Both of these values can be measured using a ruler or tape measure.

3. Can the magnification and object distance be negative values?

Yes, both magnification and object distance can be negative values. A negative magnification indicates an inverted image, while a negative object distance indicates that the object is in front of the lens.

4. What unit should I use for the magnification and object distance in the formula?

The unit used for magnification and object distance should be consistent. For example, if the object distance is measured in meters, then the magnification should also be measured in meters. It is important to use the same unit to avoid calculation errors.

5. Is it necessary to know the focal length in order to calculate magnification and object distance?

No, it is not necessary to know the focal length in order to calculate magnification and object distance. These values can be determined using other methods, such as measuring the size of the object and its image, or using a ray diagram.

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