Distance Between Lenses for a Magnification of 10

In summary, the problem involves a convex lens and a concave lens with focal lengths of 6cm and an object placed 5cm from the convex lens with a magnification of 10. Using the equations 1/f = 1/u + 1/v and magnification=v/u, we can determine that the image of the first lens is 6 times larger than the object and the image of the first lens becomes the object for the second lens. By solving for v, we can determine the distance between the two lenses. It is helpful to sketch the lenses and use 2-3 rays to determine the location and size of the image.
  • #1
clintyip
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0

Homework Statement



A convex lens and a concave lens both of 6cm focal length are placed to give an object which is 5cm from the convex lens of magnification of 10. How far are the lenses apart?

Homework Equations



1/f = 1/u + 1/v
Magnification=v/u


The Attempt at a Solution



Lens One: Convex

f=6cm
u=5cm
v=?

1/f = 1/u + 1/v
1/6 = 1/5 + 1/v
V=-30

Lens Two: Concave

f=-6 (concave)
To get a magnification of 10:
10 = v/u





That's all I have. I have no idea how to work out the distance between the two lenses. Can anyone help please?
 
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  • #2
You also have
magnification = V/U = 30/5 = 6. So the image of the first, convex lens is 6 times as large as the object.

It really helps to sketch the lenses and draw 2 or 3 rays to determine the location and size of the image. You will see what is going on if you do this.

The image of the first lens is the object for the second.
1/f = 1/u + 1/v magnification = v/u
You know f and can use the second equation to get v as a number times u. You should be able to solve these two to get a number for u. With that, you can add the second lens to your sketch and figure out the distance between the two lenses. Good luck!
 

FAQ: Distance Between Lenses for a Magnification of 10

1. What is magnification in lens physics?

Magnification in lens physics refers to the degree to which an image is enlarged or reduced when viewed through a lens. It is typically represented by the symbol "m" and is calculated by dividing the height of the image by the height of the object.

2. How is magnification related to the focal length of a lens?

Magnification is directly proportional to the focal length of a lens. This means that as the focal length increases, the magnification also increases and vice versa. This relationship is described by the equation m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.

3. What is the difference between linear and angular magnification?

Linear magnification refers to the ratio of the size of an image to the size of the object, while angular magnification refers to the ratio of the angle subtended by the image to the angle subtended by the object. Linear magnification is calculated using m = h'/h, where h' is the height of the image and h is the height of the object. Angular magnification is calculated using m = θ'/θ, where θ' is the angular size of the image and θ is the angular size of the object.

4. How does the human eye produce magnified images?

The human eye uses a combination of lenses to produce magnified images. The cornea, which is the clear outer layer of the eye, acts as a fixed lens and helps to focus light onto the retina. The lens inside the eye is able to change shape, allowing it to adjust the focal length and produce a magnified image on the retina.

5. What are some applications of magnification in lens physics?

Magnification is used in a variety of applications, including microscopy, photography, and telescopes. In microscopy, magnification allows for the visualization of small objects and structures that would otherwise be invisible to the naked eye. In photography, magnification is used to capture detailed images of distant objects. In telescopes, magnification allows us to see objects in outer space that are too far away to be seen with the naked eye.

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