Solve Lens Problem: Focal Length & Magnification

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Please do not post the same question multiple times. In summary, the conversation discusses two problems related to lens usage. The first problem involves finding the magnification when looking at a gem through a converging lens with a focal length of 13.7 cm. The second problem involves determining the distance from a nickel to a converging lens with a focal length of 17.4 cm to achieve a magnification of +2.06. The calculations for both problems are provided, but it is unclear if they are correct.
  • #1
mustang
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Lens Problems
problem 24. A person looks at a gem using a concverging lense with a focal length of 13.7 cm. The lense forms a virtual image 35.5 cm from the lense.
a) Find the magnifaction.
This is what I have done so far:
f=13.7 , q= -35.5
1/p+1/q=1/f
1/f-1/q=1/p
1/13.7-(-1/35.5)=9.88516=p
M=-q/p
=--35.5/9.88516
= 4.02333

Is this right??

Problem 30. A magnifying glass has a converging lens of focal length 17.4 cm. At what distance from a nickel should you hold this lens to get an image with a magnificaiton of +2.06? Abswer in cm.
got p=8.7 and M=1.841932169 is this right?
 
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  • #2
You posted this same problem in College Help.
 
  • #3


Yes, your calculations for both problems 24 and 30 are correct. For problem 24, the magnification is approximately 4.02, meaning the virtual image is 4.02 times larger than the object being viewed. For problem 30, the distance from the lens to the object (nickel) is approximately 8.7 cm. This means that the object should be held 8.7 cm away from the lens to achieve a magnification of +2.06. Great job!
 

1. What is the difference between focal length and magnification?

The focal length of a lens is the distance between the lens and the point where the light rays converge to form a sharp image. It is typically measured in millimeters. Magnification, on the other hand, is the ratio of the size of the image produced by the lens to the size of the object being viewed. It does not have a unit of measurement and is usually expressed as a decimal or a percentage.

2. How do I calculate the focal length of a lens?

The focal length of a lens can be calculated by measuring the distance between the lens and the image plane when the object is in focus. Alternatively, it can be calculated by dividing the distance between the lens and the object by the distance between the lens and the image.

3. What factors affect the focal length of a lens?

The focal length of a lens is determined by the curvature of the lens and the refractive index of the material it is made of. In general, lenses with a higher curvature and higher refractive index will have a shorter focal length. Additionally, the distance between the lens and the object being viewed can also affect the focal length.

4. How does the focal length of a lens impact the image produced?

The focal length of a lens is directly related to the magnification of the image produced. A shorter focal length will result in a wider field of view and a larger image, while a longer focal length will result in a narrower field of view and a smaller image. Additionally, different focal lengths can also affect the depth of field and the overall sharpness of the image.

5. Can I change the focal length of a lens?

The focal length of a lens is determined by its physical properties and cannot be changed. However, some lenses have a variable focal length, which is commonly referred to as a zoom lens. This allows the user to adjust the focal length and therefore the magnification of the lens. Additionally, the use of teleconverters and extension tubes can also alter the effective focal length of a lens.

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