# Lenses/Images - Find final image

• maniacp08
Using the thin-lens equation, we can find that the image is formed at -13.333cm to the right of the second lens.In summary, the final image is formed at -13.333cm from the second lens, with an overall lateral magnification of -0.78989581cm.
maniacp08
Lenses/Images -- Find final image

Two converging lenses, each having a focal length equal to 8 cm, are separated by 35 cm. An object is 30 cm to the left of the first lens.

(a) Find the position of the final image using both a ray diagram and the thin-lens equation

(c) What is the overall lateral magnification?

What I did:
s1' = f1s1/(s1-f1)
s1' = (8cm)(35cm)/(35cm-8cm) = 10.37cm

m1 = - s1'/s = -10.37cm/35cm = -.296285cm

s2' = f2s2/(s2-f2)
s2 = 35cm-30cm = 5cm
s2' = (8cm)(5cm)/(5cm-8cm) = -13.333cm

m2 = - s2'/s = - (-13.333cm)/5cm = 2.666cm

For question a isn't it 35cm+s1'+s2'=32.04cm or 32cm? This answer was marked wrong can anyone tell me what I did wrong?

For question c - m = m1*m2 = -.296285cm*2.666cm = -.78989581cm but this is again wrong

The first image is formed at 10.37cm to the right of the first lens.
This image is now the object for the second lens.
How far is it from the second lens?

Based on the given information, the final image is formed at a distance of 32 cm to the right of the second lens. This can be determined using the thin-lens equation: 1/f = 1/s1 + 1/s2, where f is the focal length of the lens, and s1 and s2 are the object and image distances, respectively. Plugging in the given values, we get 1/8 = 1/30 + 1/s2, which gives s2 = 40 cm. Since the object is 30 cm to the left of the first lens, the final image is formed at a distance of 30 cm + 40 cm = 70 cm to the right of the first lens. This can also be confirmed using a ray diagram, where the rays from the object will converge at this point.

For the lateral magnification, we need to take into account the magnification of both lenses. The overall lateral magnification is given by the product of the individual magnifications, which in this case is (-0.296285)(2.666) = -0.7898. This indicates that the final image is smaller and inverted compared to the original object. However, the negative sign indicates that the final image is on the opposite side of the lens, which is to the right in this case. So the final image is smaller and inverted, located 70 cm to the right of the first lens.

## 1. How do lenses create images?

Lenses create images through a process called refraction, where light rays passing through the lens are bent and converge at a focal point. This results in an inverted and magnified image being formed on the opposite side of the lens.

## 2. What factors affect the final image produced by a lens?

The final image produced by a lens is affected by several factors, including the focal length of the lens, the distance between the object and the lens, and the type and quality of the lens itself. Additionally, factors such as lighting and the properties of the object being photographed can also impact the final image.

## 3. How can I calculate the final image produced by a lens?

To calculate the final image produced by a lens, you will need to know the focal length of the lens, the distance between the object and the lens, and the magnification of the lens. You can then use the lens equation, 1/f = 1/o + 1/i, to determine the size and location of the final image.

## 4. Can different lenses produce different types of images?

Yes, different lenses can produce different types of images. This is because each lens has its own unique characteristics and properties, such as focal length and aperture size, which can affect the quality and type of image produced. For example, a wide-angle lens will produce a different image than a telephoto lens, even when photographing the same subject.

## 5. What are some common types of lens aberrations and how do they affect images?

Some common types of lens aberrations include chromatic aberration, spherical aberration, and distortion. These aberrations can cause images to appear blurry, distorted, or have color fringes. To minimize these effects, high-quality lenses are designed with multiple elements and coatings to correct for aberrations.

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