Optics question: What two positions of a lens gives a sharp image?

In summary, the problem involves a lamp and a screen that are 1m apart and a +4.5 D thin lens placed between them. The question is where the lens must be placed to produce a sharp image on the screen, and what the magnification will be. Using the Gauss Law, the possible positions of the lens are found to be at F or F', but neither work. The correct law is actually n/l + F = n'/l' and using this, two possible positions for the lens are found, resulting in magnifications of -2 and -1/2.
  • #1
LeeLoo
3
0
1. A lamp and a screen are 1m apart and a +4.5 D thin lens is mounted between them. Where must the lens be placed in order to produce a sharp image on the screen, and what will be the magnification?



2. Gauss Law: L' = L + F



3. I attempted this question by using the Gauss Law but I just don't know how to find the two possible positions of the lens to give a sharp image. I thought that a sharp image might be formed at F or F' but it doesn't work. Can someone please show me how to do this problem and explain it :)
 
Physics news on Phys.org
  • #2
LeeLoo said:
I thought that a sharp image might be formed at F or F' but it doesn't work.
Why doesn't it work? What do you know about "F" ?
 
  • #3
Welcome to PF!

LeeLoo said:
Gauss Law: L' = L + F

Hi LeeLoo! Welcome to PF! :smile:

I don't think that's the right law …

shouldn't it have 1/… ? :wink:
 
  • #4
Oh, yeah, the law is actually n/l + F = n'/l' but i thought people could abbreviate it like that. anyway, yay, i know how to do the question now!

1/l' + 1/l = F
l' +l =1m
l' = 1 - l

so sub that in and get two answers for 'l' which are the lens positions :D

and magnification= l'/l so you get m = -2 or -1/2

COOL!
 

1. What is the difference between the focal length and the focal point of a lens?

The focal length of a lens is the distance between the lens and its focal point. The focal point is the point where parallel rays of light converge after passing through the lens. In other words, the focal length determines the strength of the lens, while the focal point is the actual point where the image is formed.

2. How do you determine the optimal distance between a lens and an object to get a sharp image?

The optimal distance between a lens and an object can be determined by using the thin lens equation: 1/f = 1/o + 1/i, where f is the focal length of the lens, o is the distance between the lens and the object, and i is the distance between the lens and the image. By rearranging the equation, you can solve for i to determine the optimal distance.

3. Can a lens have more than one focal point?

Yes, a lens can have more than one focal point. This is known as a multi-focal lens, and it is commonly used in bifocals or progressive lenses for glasses. These lenses have multiple focal points to correct for different vision needs, such as nearsightedness and farsightedness.

4. How does the shape of a lens affect the formation of a sharp image?

The shape of a lens can affect the formation of a sharp image by altering the path of light rays as they pass through the lens. Convex lenses, which bulge outwards, converge light rays to form a sharp image, while concave lenses, which curve inward, diverge light rays and create a distorted image.

5. Can a lens produce a sharp image with only one position?

No, a lens needs to be in two positions to produce a sharp image. The first position is where the object is placed at the optimal distance from the lens, and the second position is where the image is formed on a screen or retina. Without both of these positions, the image will not be sharp.

Similar threads

Understanding a Converging Lens and Its Two Positions
    • Introductory Physics Homework Help
Replies
3
Views
1K
Image position in an optical system?
    • Introductory Physics Homework Help
Replies
5
Views
1K
When is the image produced by a thin lens sharp?
    • Introductory Physics Homework Help
Replies
1
Views
1K
Position of the object and image in this optics problem
    • Introductory Physics Homework Help
Replies
10
Views
1K
Inserting thick lenses into a thin lens system and deducing values
    • Introductory Physics Homework Help
Replies
1
Views
947
Imaging resolution for a microscope and eye
    • Introductory Physics Homework Help
Replies
5
Views
841
Image with an Plano-Convex lens
    • Introductory Physics Homework Help
Replies
7
Views
2K
What is the focal length of the lens?
    • Introductory Physics Homework Help
Replies
20
Views
2K
Splitting of a convex lens problem
    • Introductory Physics Homework Help
Replies
5
Views
1K
Measurement of Focal length with Laser beam
    • Introductory Physics Homework Help
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top