# Object in front of two lenses

• Rawr
In summary, the conversation discusses the placement of objects and lenses in relation to each other and the resulting image. With the given parameters, the final image is located at a distance of 1.395 m and has a height of 1.4 cm with an inverted orientation. The conversation also mentions the importance of inverting the final distance and taking into account the effects of both lenses for calculating the final magnification.
Rawr
A 1.5-cm tall object is placed 0.50 m to the left of a diverging lens with a focal length of 0.20 m. A converging lens with a focal length of 0.17 m is located 0.08 m to the right of the diverging lens. What is the height and orientation with respect to the original object of the final image.

Okay, first, I find the distance of the image with respect to the diverging lens first.

-1/.2 = 1/di + 1/.5
di = -0.1428...

Then, I add that distance image to the converging lens distance to get the object distance for the converging lens.

0.08 + -.1428.. = .2228 m

Then I use the lens equation again except with that object distance and the focal length of the converging lens.

1/.17 = 1/di + 1/.2228
di = 1.395...

Then I take the magnification equation and use hi/h0 = -di/d0

hi / (1.5) = -(1.395)/(.5)
Solve for hi.. and get -4.185.

Apparently, that is not the answer. The answer key says that it is 1.4 cm with an inverted image. I don't really know how they get 1.4. Where did I go wrong in my work? Or am I wwwaaayy off with what I'm doing?

For your final di of 1.395 I think you forgot to invert it. It should be 1/1.395.
For the magnification, find the magnification due to the first lens, and then the second lens. The product of the two will give you the final magnification. Your way won't work because after the first lens, the size of the object is not 1.5 cm anymore. Also the object distance changes after the first lens. Work that out and see what you get.

Your calculations seem correct, but it's possible that there is a mistake in the given answer or in the steps leading up to it. It's always important to double check your work and make sure all the values and equations are correct. If you are confident in your calculations, you may want to bring this discrepancy to the attention of your instructor or the person who provided the question. They may be able to clarify or correct the answer.

## 1. What is the purpose of using two lenses when observing an object?

The use of two lenses in an optical system allows for greater magnification and clarity of the object being observed. The first lens, known as the objective lens, captures the light from the object and creates a real image. The second lens, known as the eyepiece, magnifies this image for the viewer to see.

## 2. How does the distance between the lenses affect the image of the object?

The distance between the lenses, also known as the focal length, determines the magnification and orientation of the image. A shorter focal length will result in a larger and upside-down image, while a longer focal length will result in a smaller and right-side-up image.

## 3. Can the object be seen without using two lenses?

Yes, an object can still be seen without using two lenses. However, using two lenses allows for a clearer and more magnified image of the object. It also allows for the use of various optical instruments, such as microscopes and telescopes, which rely on the use of two lenses.

## 4. What is the difference between convex and concave lenses?

Convex lenses are thicker in the middle and thinner at the edges, causing light rays to converge and creating a real image. Concave lenses are thinner in the middle and thicker at the edges, causing light rays to diverge and creating a virtual image. In an optical system, convex lenses are typically used as the objective lens and concave lenses as the eyepiece.

## 5. How does the shape of the lenses affect the image of the object?

The shape of the lenses affects the way light rays are refracted, which in turn affects the image of the object. Convex lenses bend light rays towards the center, resulting in a magnified image. Concave lenses bend light rays away from the center, resulting in a smaller and upright image. The curvature of the lenses also determines the amount of distortion in the image.

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