Creating an Image 2x Size of Object w/ Convex Lens: Half Focal Length Away

In summary, a converging lens (convex lens) creates an image that is two times the size of the object when the object is placed at a distance of half the focal length in front of the lens. This can be represented mathematically by the equation 1/f = 1/di + 1/do, where f is the focal length, di is the image distance, and do is the object distance. It is important to carefully consider the given information and equations when solving problems involving lens systems.
  • #1
Gear2d
51
0

Homework Statement


A converging lens (convex lens) creates an image that is 2 times the size of the object. The object is placed:


Homework Equations



-di/do = hi/ho
1/f = 1/di + 1/do

The Attempt at a Solution



I thought the answer was that the object is place two focal lengths in front of the lens. But the answer says its half a focal length in front of the lens.

I mean: -di/do = hi/ho = 2
-di = 2do
1/f = 1/di + 1/do
= -1/2do + 1/do = 1/2do
f = 2do

Isn't f=2do saying two focal lengths?
 
Last edited:
Physics news on Phys.org
  • #2
Gear2d said:

Homework Statement


A converging lens (convex lens) creates an image that is 2 times the size of the object. The object is placed:


Homework Equations



-di/do = hi/ho
1/f = 1/di + 1/do

The Attempt at a Solution



I thought the answer was that the object is place two focal lengths in front of the lens. But the answer says its half a focal length in front of the lens.

I mean: -di/do = hi/ho = 2
-di = 2do
1/f = 1/di + 1/do
= -1/2do + 1/do = 1/2do
f = 2do

Isn't f=2do saying two focal lengths?

I'm not sure what you mean. If [itex]f=10[/itex] for example, then [itex]d_o=5[/itex], so [itex]d_o[/itex] is half the focal length.
 
  • #3
So simple, thanks. I guess I just missed an easy answer by thinking too much (or thinking to less).

Thanks again
 
  • #4
Gear2d said:
Isn't f=2do saying two focal lengths?

No.

f=2do is saying do=f/2, or half a focal length.

(do=2f would be saying two focal lengths.)
 

What is the concept behind creating an image 2x size of object with a convex lens?

The concept behind creating an image 2x size of object with a convex lens is based on the principle of refraction, where light rays passing through a convex lens are bent towards its center. This causes the image to appear magnified when viewed from a certain distance.

What is the focal length of a convex lens and how does it affect the size of the image?

The focal length of a convex lens is the distance between the lens and its focal point. The shorter the focal length, the larger the magnification of the image will be. In this case, placing the object half the focal length away from the lens will result in an image that is 2x the size of the object.

What factors can affect the clarity and quality of the enlarged image?

The clarity and quality of the enlarged image can be affected by several factors such as the curvature and quality of the lens, the distance between the lens and the object, and the lighting conditions. Any imperfections in the lens or improper positioning of the object can result in a distorted or blurry image.

Can this method be used to create an image that is smaller than the original object?

Yes, this method can also be used to create an image that is smaller than the original object. This can be achieved by placing the object closer to the lens than the focal length. In this case, the image will appear smaller and inverted.

How is this principle applied in real-world applications?

The principle of creating an enlarged image with a convex lens is widely used in optical instruments such as magnifying glasses, microscopes, and telescopes. It is also used in photography to create larger images of distant objects. In addition, it is utilized in industries such as medicine and biology for magnifying tiny structures and organisms for study and analysis.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
696
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
7K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
960
  • Introductory Physics Homework Help
Replies
3
Views
822
Back
Top