Why is the image distance negative in a Two Thin Lens setup?

In summary, when two 25.0 cm focal length converging lenses are placed 16.5 cm apart and an object is placed 35.0 cm in front of one lens, the final image formed by the second lens will be located at -71 cm, which is to the left of the second lens. This is because the image distance is negative when the image is formed on the opposite side of the lens from the object. This can be understood through the equation 1/f = 1/o + 1/i, where f is the focal length, o is the object distance from the lens, and i is the image distance from the lens.
  • #1
whitehorsey
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1. Two 25.0 cm focal length converging lenses are placed 16.5 cm apart. An object is placed 35.0 cm in front of one lens. Where will the final image formed by the second lens be located?

I got the right answer but I'm not sure why the image distance is negative when the image (formed by the first lens) is to the right of the converging lens.
2. 1/f = 1/o + 1/i, where f = focal length, o = object distance from lens, i = image distance from lens.
3. I've done all the steps but I'm just not sure why the image distance is negative for the image formed from the first lens.

Here is my work:
1/f = 1/o + 1/i
1/25 = 1/35 + 1/i
i = 87.5 cm to the right of lens 1, which is 71 cm to the right of lens 2.

However, the answer to the image distance (from the first lens) was -71 cm, not +71 cm.

Can you explain this to me please?
 
Last edited:
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  • #2
It is best explained by a diagram.
 

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  • diagram - virtual object.pdf
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What is a thin lens?

A thin lens is a transparent material with curved surfaces that is used to refract (bend) light rays. It is typically made of glass or plastic and can have either a convex or concave shape.

What is the difference between a convex and concave lens?

A convex lens is thicker in the middle and thinner at the edges, causing light rays to converge (come together) after passing through it. A concave lens is thinner in the middle and thicker at the edges, causing light rays to diverge (spread out) after passing through it.

How do you calculate the focal length of a thin lens?

The focal length of a thin lens can be calculated using the lensmaker's formula: 1/f = (n-1) * (1/R1 - 1/R2), where f is the focal length, n is the refractive index of the lens material, R1 is the radius of curvature of one surface, and R2 is the radius of curvature of the other surface.

What is the difference between a real and virtual image?

A real image is formed when light rays actually converge at a point, allowing the image to be projected onto a screen. It is always inverted and can be captured by a camera or seen with the naked eye. A virtual image, on the other hand, is formed when light rays appear to converge at a point, but do not actually do so. It is always upright and cannot be captured on a screen.

How do thin lenses interact with each other?

When two thin lenses are placed close together, the second lens will create a new image from the first lens' image. This is known as the principle of superposition. The new image can be either real or virtual, and its distance from the second lens can be calculated using the thin lens formula: 1/u + 1/v = 1/f, where u is the object distance, v is the image distance, and f is the focal length.

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