# Solving Optic Lens Problem: Find Object Distance for Magnification of 75

• mithil03
In summary, the problem is asking for the distance in front of the first lens that the object should be placed in order for the image to be magnified by a factor of 75. To solve this, we can use the lens equation: 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the distance from the object to the lens, and d_i is the distance from the lens to the image. The lens equation can be rearranged to solve for d_i: d_i = (f*d_o)/(d_o-f). For the second question, the lens has a thickness and we cannot use the thin lens approximation. We would need to use the thick lens equation
mithil03

## Homework Statement

Suppose we have a microscope made out of two lenses, both with a focal length of
25mm, placed 36.5mm apart. Find how far in front of the first lens should the object be
placed to assure that the image is magnified at least by a factor of 75?

One more:
Suppose that we have a positive lens with radii 60 and 100 and thickness of 3 (any units,
as long as you are consistent), with an index of 1.5. If an object with a height of 10 is
placed at a distance of 100 from the lens, find at what distance from the back surface is
the image formed. DO NOT treat this as a thin lens.

## The Attempt at a Solution

The first one, couldn't understand how to calculate for magnification factor of 75

mithil03 said:

## Homework Statement

Suppose we have a microscope made out of two lenses, both with a focal length of
25mm, placed 36.5mm apart. Find how far in front of the first lens should the object be
placed to assure that the image is magnified at least by a factor of 75?

One more:
Suppose that we have a positive lens with radii 60 and 100 and thickness of 3 (any units,
as long as you are consistent), with an index of 1.5. If an object with a height of 10 is
placed at a distance of 100 from the lens, find at what distance from the back surface is
the image formed. DO NOT treat this as a thin lens.

## The Attempt at a Solution

The first one, couldn't understand how to calculate for magnification factor of 75

Why didn't you list the lens equation as a Relevant Equation? That's why we have that line in the Homework Help Template.

List the Lens Equation, and show your work to solve the first question.

Then, what is different about the 2nd question? What equations apply when you can't use the thin lens approximation?

We do not do your work for you here at the PF. We can offer hints and ask questions, but we do not open your textbook for you and do your reading...

## 1. How do I determine the object distance for a magnification of 75?

The object distance can be found by using the formula: 1/f = 1/o + 1/i, where f is the focal length of the lens, o is the object distance, and i is the image distance. Rearrange the formula to solve for o: o = (f*i)/(i-f). Plug in the known values for f (found on the lens) and i (75 times the object distance) to find the object distance.

## 2. What is the significance of a magnification of 75?

A magnification of 75 means that the image produced by the lens will be 75 times larger than the actual object. This is useful in applications such as microscopy or telescopes where we want to see small objects in greater detail.

## 3. How does the focal length of the lens affect the object distance for a magnification of 75?

The focal length of the lens is directly proportional to the object distance. This means that as the focal length increases, the object distance also increases. Therefore, for a magnification of 75, a lens with a longer focal length will have a larger object distance compared to a lens with a shorter focal length.

## 4. Can I use any lens to achieve a magnification of 75?

No, not all lenses are capable of producing a magnification of 75. The magnification of a lens is determined by its focal length and the distance between the object and the lens. Therefore, you will need to use a lens with a specific focal length and place the object at a specific distance in order to achieve a magnification of 75.

## 5. What other factors should I consider when solving optic lens problems?

Other factors to consider include the type of lens (convex or concave), the material of the lens (glass, plastic, etc.), and the size of the lens. These factors can affect the focal length and therefore, the object distance needed to achieve a specific magnification. Additionally, the position and orientation of the lens in relation to the object and the eye also play a role in solving optic lens problems.

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