# Object distance and magnifiation

• 996gt2
In summary, the conversation discusses how to determine the object distance needed to achieve a lateral magnification of -40 with a 6mm diameter microscope objective with a focal length of 9mm. The equation mobj=-L/fobj is used to solve for the object distance, but it is found to be incorrect. The correct approach is to use the Gaussian lens formula, which takes into account the small object distance and the short length of the microscope tube. Using this formula, the object distance is determined to be 9.225mm, which is significantly different from the initial estimate of 360mm.
996gt2

## Homework Statement

A 6mm diameter microscope objective has focal length 9mm.

What object distance is required to achieve a lateral magnification of -40?

mobj=-L/fobj

## The Attempt at a Solution

-40x=-L/9mm

L=360mm

Why isn't the answer 360mm? I think it might have something to do with the diameter of the lens, but I'm not completely sure. Can someone explain? Thanks!

Anyone?

Well, the formula I included is basically an approximation derived from the Gaussian lens formula...at least, that's how my book put it.

Basically, with a microscope, the object is very very close to the focal point, so s$$\approx$$f. Similarly, the focal length of the objective is much less than the length of the microscope tube, so s'$$\approx$$L

Is it wrong to use these adapted formulas from the book?

Yes, the object distance will be close to f=9mm. So your answer of 360mm is way way off.

Hmmm, after some thinking I got:

$$1/f=1/s+1/s'$$
$$1/9mm=1/x+1/40x$$
$$x=9.225mm$$

And it was right! Thanks for the suggestion to use the Gaussian optics formulas :)

## 1. What is object distance?

Object distance refers to the distance between the object being observed and the lens of a microscope or telescope. It is measured in millimeters (mm) or centimeters (cm) depending on the scale used.

## 2. How does object distance affect magnification?

The closer the object is to the lens, the larger it will appear, resulting in a higher magnification. Conversely, a further object distance will result in a smaller image and lower magnification.

## 3. What is magnification?

Magnification is the process of making an object appear larger than its actual size. It is achieved by using lenses or other optical devices.

## 4. How is magnification calculated?

Magnification is calculated by dividing the size of the image by the size of the object. For example, if the size of the image is 10mm and the size of the object is 2mm, the magnification would be 5x (10mm/2mm = 5).

## 5. Is there a relationship between object distance and field of view?

Yes, there is a relationship between object distance and field of view. As the object distance increases, the field of view also increases, resulting in a wider view of the object. This is why adjusting the focus of a microscope or telescope can change the field of view.

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