# Object Distance & Magnification: Explained w/Diagram

• MHB
• MermaidWonders
In summary, the problem involves an object and its lens-produced real image that are 2.4 m apart. The lens has a focal length of 55 cm. To find the values for the object distance and magnification, we can use the formulas $\frac{1}{{d}_{o}} + \frac{1}{{d}_{i}} = \frac{1}{f}$ and $m = -\frac{{d}_{i}}{{d}_{o}}$. Solving the set of equations, we get the possible values for object distance and magnification. The distances add up to a total distance between the object and image, considering that they can both be on different sides of the lens.
MermaidWonders
An object and its lens-produced real image are 2.4 m apart. If the lens has 55-cm focal length, what are the possible values for the object distance and magnification?

Can someone please explain this with a diagram of the different possibilities (or, if not, just give a detailed explanation on how one should approach this)?

Last edited:
MermaidWonders said:
An object and its lens-produced real image are 2.4 m apart. If the lens has 55-cm focal length, what are the possible values for the object distance and magnification?

Can someone please explain this with a diagram of the different possibilities (or, if not, just give a detailed explanation on how one should approach this)?

Attempt?
Which formula applies?

I like Serena said:
Attempt?
Which formula applies?

Well, formulas $\frac{1}{{d}_{o}} + \frac{1}{{d}_{i}} = \frac{1}{f}$ and $m = -\frac{{d}_{i}}{{d}_{o}}$ probably apply... I just have trouble finding ${d}_{o}$ and ${d}_{i}$ given that the object and its image are 2.4 m apart...

MermaidWonders said:
Well, formulas $\frac{1}{{d}_{o}} + \frac{1}{{d}_{i}} = \frac{1}{f}$ and $m = -\frac{{d}_{i}}{{d}_{o}}$ probably apply... I just have trouble finding ${d}_{o}$ and ${d}_{i}$ given that the object and its image are 2.4 m apart...

Good! It means that we have the set of equations:
\begin{cases} d_o+d_i=2.4 \text{ m} \\
f = 0.55 \text{ m}\\
\frac 1{d_o} + \frac 1 {d_i} = \frac 1f \\
m=\left| \frac{d_i}{d_o}\right|
\end{cases}
Can you solve it? (Wondering)

I like Serena said:
Good! It means that we have the set of equations:
\begin{cases} d_o+d_i=2.4 \text{ m} \\
f = 0.55 \text{ m}\\
\frac 1{d_o} + \frac 1 {d_i} = \frac 1f \\
m=\left| \frac{d_i}{d_o}\right|
\end{cases}
Can you solve it? (Wondering)

I keep thinking that ${d}_{o} - {d}_{i}$ is 2.4 m... I didn't know they add up to be 2.4 m... Why?

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MermaidWonders said:
I keep thinking that ${d}_{o} - {d}_{i}$ is 2.4 m... I didn't know they add up to be 2.4 m... Why?

Normally the object and image are at different sides of the lense, meaning their distances add up.
However, it is possible that we have a virtual image that is on the same side of the lense as the object.
In that case we treat the image distance as a negative distance.
Either way, to do the math, we treat them as adding up to a total distance between object and image.

I like Serena said:
Normally the object and image are at different sides of the lense, meaning their distances add up.
However, it is possible that we have a virtual image that is on the same side of the lense as the object.
In that case we treat the image distance as a negative distance.
Either way, to do the math, we treat them as adding up to a total distance between object and image.

Oh, I see. I'll try that. :)

## 1. What is the relationship between object distance and magnification?

The object distance and magnification have an inverse relationship. As the object distance increases, the magnification decreases. Similarly, as the object distance decreases, the magnification increases.

## 2. How is object distance measured in microscopy?

The object distance is measured as the distance between the object being viewed and the objective lens of the microscope. It is usually measured in millimeters or micrometers.

## 3. What is the difference between magnification and resolution?

Magnification refers to the increase in apparent size of an object when viewed through a microscope. Resolution, on the other hand, refers to the ability of a microscope to distinguish between two closely spaced objects. In other words, magnification makes an object appear larger, while resolution makes it appear clearer and more detailed.

## 4. How does changing the objective lens affect the magnification?

The magnification of a microscope is determined by the objective lens. By changing the objective lens to one with a higher magnification, the overall magnification of the microscope increases. However, this also results in a decrease in the field of view and depth of field.

## 5. Why is object distance important in microscopy?

The object distance is important in microscopy because it affects the magnification and resolution of the microscope. Choosing the right object distance is crucial in obtaining clear and detailed images. Additionally, adjusting the object distance can also help in correcting any distortions or aberrations in the image.

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