Distance from the object to objective lens and focal length

In summary, the focal length of the medium-power objective lens in a laboratory microscope is 3.70mm and it produces a lateral magnification of -42.5. To find the "working distance," the distance from the object to the objective lens, we can use the formula m=-di/fobjective. However, this formula assumes that the object distance (do) is approximately equal to the focal length (fobjective). If we draw a ray diagram, we can see that this is not the case and we cannot use this formula. To find the working distance, we can use the formula m=-di/fobjective and solve for di. For the second question, we can use the same formula and solve for the focal length of the
  • #1
bubothedog
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Homework Statement


1) The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.70mm . If this lens produces a lateral magnification of -42.5, what is its "working distance"; that is, what is the distance from the object to the objective lens?
2)
What is the focal length of an eyepiece lens that will provide an overall magnification of -130? Assume student's near-point distance is N = 25 cm

Homework Equations



m=-di/fobjective

The Attempt at a Solution


I tried using that formula to solve for this distance for object but it doesn't work out. I got that formula from a book where they assume that do is approx to be fobjective. Tbh, I don't quite understand how to get this "working distance". Anyone can help?
 
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  • #2
Have you drawn a ray diagram? It should help you understand how "m=-di/fobjective" can be derived and thus, help you understand the question.
 

1. How does the distance from the object to the objective lens affect the focal length?

The distance from the object to the objective lens directly affects the focal length of a lens. The closer the object is to the lens, the shorter the focal length will be, while a greater distance will result in a longer focal length. This is because the angle at which light rays enter the lens changes depending on the distance, which in turn affects the convergence of the light rays and the focal point.

2. What is the relationship between the distance from the object to the objective lens and the magnification of an image?

The distance from the object to the objective lens is directly proportional to the magnification of an image. This means that as the distance from the object increases, the magnification of the image also increases. This is because a greater distance results in a larger image being projected onto the focal plane, resulting in a larger magnification.

3. How does the distance from the object to the objective lens affect the depth of field?

The distance from the object to the objective lens has a significant impact on the depth of field. The closer the object is to the lens, the shallower the depth of field will be, meaning that only a small portion of the image will be in focus. On the other hand, a greater distance results in a deeper depth of field, allowing more of the image to be in focus.

4. Is there an ideal distance from the object to the objective lens for achieving optimal image quality?

Yes, there is an ideal distance from the object to the objective lens for achieving optimal image quality. This distance is known as the "optimal working distance" and it varies depending on the specific lens being used. Generally, it is recommended to keep the object at a distance that is slightly greater than the focal length of the lens for the best image quality.

5. Can the distance from the object to the objective lens be adjusted for different types of lenses?

Yes, the distance from the object to the objective lens can and should be adjusted for different types of lenses. Each lens has a specific focal length and optimal working distance, and adjusting the distance can greatly impact the resulting image. For example, a macro lens will require a much closer distance to the object compared to a telephoto lens in order to achieve optimal image quality.

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