# Image Formation by Lenses

Have a look at the photos below. They show two different examples of image formation by lenses One shows the image of a house, inverted and diminished. And the other shows the image of a postage stamp, enlarged and upright. You may think the lenses used are very different since the images are, but they are the same lens! If you have a magnifying glass at home, you can verify that the images formed change with the distance.

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Table of contents

Wonder why this happens? Then keep reading. We will talk about different lenses and explain how they work. Then we will use basic rules to describe image formation by lenses.

## How does an image form when using lenses?

Lenses work by using the refraction of light.

Refraction is the deviation of light when it goes from one medium to another due to light propagating at different speeds on them.

Light changes its direction when it goes through a water-air interface because it moves slower in water than in air. This is why an object looks bent when it is partially submerged in a glass of water. The light coming from the submerged part appears to come from a different position than it really does.

The light coming from the submerged part appears to come from a different position than it really does making the pen look bent.

Light gets refracted when interacting with the lens because it moves through the air and the lens at different speeds. Depending on the lens's shape, an object's light can converge to a point or diverge from it, forming an image.

## Types of images formed by lenses

We can classify the images formed by lenses as real or virtual.

### Types of images formed by lenses: Real Images

A real image is formed by light rays actually converging or diverging from a source.

A real image can be projected on a screen.

The light rays of an object that reflect on a concave mirror produce a real and inverted image. Since the image is real, we can project it on a paper sheet by placing it where the image forms.

Light rays reflected from a spherical concave mirror form a real image that can be projected on a screen. Cymru.lass Public Domain.

### Types of images formed by lenses: Virtual images

A virtual image forms when the light rays appear to come from a source that is not really there.

We can't project virtual images because the light rays of a virtual image do not converge.

Plain mirrors produce virtual images. The light rays from an object reflect onto our eyes, giving the impression of converging at the back of the mirror. However, the source is in front of the mirror.

A spectator can see a virtual image when looking into a mirror. CC-BY-SA-4.0

One of the most important properties of an image is its magnification.

Magnification quantifies how much an image's size changes with respect to the object's size.

We can measure magnification using the following formula.

$\text{magnification =}\frac{\text{image height}}{\text{object height}}$

Since the magnification is a ratio it has no units.

Consider an object$4\mathrm{cm}$ tall. If a lens produces an image with a height of$12\mathrm{cm}$, calculate the magnification.

$\mathrm{magnification}=\frac{\mathrm{image}\mathrm{height}}{\mathrm{object}\mathrm{height}}=\frac{12\overline{)\mathrm{cm}}}{3\overline{)\mathrm{cm}}}=4$

The magnification of the image is$4$, which means it is four times larger than the object.

## Image formation by convex lenses

A convex lens or converging lens refracts all rays of light parallel to its principal axis onto a single point called the principal focus.

The principal axis is an imaginary horizontal line that goes through the geometric centre of a lens.

A convex lens is curved or rounded outwards.

Light rays parallel to the principal axis converge at the focus, StudySmarter Originals

Note that light refracts as it goes from the air into the lens and again as it goes back into the air. Since we can use the lens in both directions, we can identify two foci at the same distance from the lens's geometrical centre - also called the optical centre. The distance from the lens centre to its focus is called focal distance.

The focal length is the distance from the focus to the geometrical centre of the lens. StudySmarter Originals

We can understand how convex lenses form images using ray diagrams. Ray diagrams consider that light rays only refract at one point and use a simpler representation for the lens. Below is a ray diagram representing the same convex lens shown before. We can label the foci as${F}_{1}$and${F}_{2}$.

In a ray diagram, a convex lens is represented using a line segment with two arrow heads pointing outward on its ends. StudySmarter Originals

In general, a convergent lens is thicker in the middle.

Converging lenses are thicker in the middle than the edges, StudySmarter Originals

### Rules for image formation by convex lenses

The behaviour of the light rays that go through a convex lens can be summarized as three basic rules.

1. Light rays parallel to the principal axis refract passing through the focus on the other side.
2. Light rays that go through the optical centre don't deflect.
3. Light rays passing through the focus refract parallel to the principal axis.

The behaviour of light rays going through a convex lens can be simplified by considering three special cases. StudySmarter Originals

## Examples of image formation by convex lenses

We can have different types of image formation when using a convex lens. The properties of the images formed depend on the object's distance,$O$. We can distinguish five cases:

1. The object is beyond two focal distances$\left(O>2{\mathrm{F}}_{2}\right)$.
2. The object is exactly at two focal distances$\left(O=2{\mathrm{F}}_{2}\right)$.
3. The object is between one and two focal distances$\left({\mathrm{F}}_{2}.
4. The object at the focus$\left(O={\mathrm{F}}_{2}\right)$.
5. The object is between the focus and the lens$\left(O<{\mathrm{F}}_{2}\right)$.

### Case 1: Object placed beyond two focal distances

We can find the image's position by drawing two light rays from the top of the object. The top of the image will be where these rays meet. Let's draw two light rays using rules 1 and 3.

Image formation by a convex lens for an object placed beyond two focal distances. Adapted from Kvr.lohith (CC BY-SA 4.0)

In this case, the image is:

• Real
• Diminished
• Inverted
• Formed beyond the focus but before two focal distances.

This is the same example of image formation as in the photo showing the image of a house at the beginning of the article!

### Case 2: Object placed exactly at two focal distances

Let's repeat the same procedure. For this case, the image is:

• Real and inverted
• Same size as the object
• Formed at exactly two focal distances

Image formation by a convex lens for an object at 2F1. Adapted from Kvr.lohith (CC BY-SA 4.0)

### Case 3: Object placed between one and two focal distances

Under these conditions, the image is:

• Real
• Inverted
• Enlarged
• Formed beyond two focal distances

Image formation by a convex lens for an object placed between F2 and 2F2. Adapted from Kvr.lohith (CC BY-SA 4.0)

### Case 4: Object placed at the focus

This case is peculiar. The light rays are parallel after refracting and never intersect. Therefore, we say the image forms at infinity.

Image formation by a convex lens for an object placed at F2 on the principal axis. Adapted from Kvr.lohith (CC BY-SA 4.0)

The image formed will be:

• Real
• Inverted
• Highly enlarged
• Formed at infinity

### Case 5: Object placed between the focus and the lens

In this case, the refracted rays don't intersect and move away from each other. However, if we extend the light rays backwards, they intersect behind the object. This is a different type of image formation. The light rays appear to come from behind the lens. Since the light rays do not really intersect the image is virtual.

Image formation by a convex lens for an object placed between F2 and the optical centre. Adapted from Kvr.lohith (CC BY-SA 4.0)

In this case, the image produced will be:

• Virtual and upright
• Magnified
• Behind the object

Magnifying glasses are an application of this case. That is why they can make enlarged images. This is the same example of image formation as in the photo of the stamp's image at the beginning of the article!

## Correcting farsightedness with convex lenses

When we see an object, its light goes through a transparent structure in our eyes - the cornea - and then through a crystalline lens. Our eyes adjust the thickness of this lens so that incoming light rays converge exactly at the retina, where we have special cells acting as light receptors. However, specific eye issues can affect this process.

Farsightedness or hyperopia is a condition where a person can see faraway objects clearly but see nearby objects blurry.

The eyes of a person with farsightedness converge the light rays of near objects behind the retina, perceiving a blurry image.

A farsightedness person sees near objects blurry as their light converges behind the retina, StudySmarter Originals

This condition can be corrected by using a converging lens which helps the eyes to converge the light rays at a shorter distance, allowing them to focus on the retina.

Convex lenses help by converging the light rays so that the eyes can form the image at the retina, StudySmarter Originals

## Image formation by concave lenses

A concave lens or diverging lens disperses the light rays parallel to the principal axis after refraction looking as if they were emerging from one point called the principal focus.

Concave lenses are hollowed out or rounded inwards. The following image illustrates how light rays passing through a concave lens disperse.

A concave lens makes the light rays diverge. StudySmarter Originals

The following ray diagram represents the same situation.

In a ray diagram, a concave lens is represented using a line segment with two arrowheads pointing inwards on its ends. StudySmarter Originals

In general, a divergent lens is thicker on its edges.

Divergent lenses can have different forms, but they are thinner in the middle than in the edges, StudySmarter Originals

### Rules for Image formation by concave lenses

We can summarize the behavior of light rays as going through concave lenses as three rules.

1. Light rays parallel to the principal axis diverge appearing to come from the focus.
2. Light rays going through the optical center don't deviate.
3. Light rays going towards the focus refract moving parallel to the principal axis.

The behaviour of light rays going through a concave lens can be simplified by considering three special cases. StudySmarter Originals

## Example of image formation by concave lenses

Have a look at the picture below for an object between one and two focal distances. Tracing two rays according to the previous rules we can see that light rays appear to intersect in front of the object.

Image formation by a concave lens. Kvr.lohith (CC BY-SA 4.0)

The image formed by the concave lens is:

• Virtual and upright
• Diminished
• Formed between the object and the lens

For a concave lens, the object's position does not matter. We always obtain the same type of image formation as the properties of the image are always the same.

## Correcting nearsightedness with concave lenses

Nearsightedness or myopia is a condition where a person can clearly see near objects, but not distant ones.

The eyes of a person with nearsightedness converge light rays in front of the retina, resulting in a blurry image.

A person with nearsightedness or myopia converges the light rays of distant objects in front of the retina. StudySmarter Originals

We can correct this using concave lenses. These lenses disperse the light rays so that the eyes can converge the light at the retina.

Concave lenses help by dispersing the light rays so the eyes can converge them at the retina, StudySmarters Originals

## Image Formation by Lenses - Key takeaways

• Convex lenses are curved or rounded outwards and converge light rays.

• Concave lenses are hollowed out or rounded inwards and disperse light rays.

• For convex lenses,

1. Light rays parallel to the principal axis refract passing through the focus on the other side.
2. Light rays that go through the optical centre don't deflect.
3. Light rays passing through the focus refract parallel to the principal axis.
• Images formed by a convex lens have different properties depending on the object's placement.
• For concave lenses,
1. Light rays parallel to the principal axis diverge appearing to come from the focus.
2. Light rays going through the optical center don't deviate.
3. Light rays going towards the focus refract moving parallel to the principal axis.
• Images formed by a concave lens are always virtual and upright and form between the object and the lens regardless of the object's position.
• A person with farsightedness or hyperopia can usually see faraway objects clearly, but not nearby objects. This issue can be resolved using convex lenses.
• A person with nearsightedness or myopia can see near objects clearly, but not distant ones. This issue can be resolved using concave lenses.

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##### Frequently Asked Questions about Image Formation by Lenses

What kind of image is formed by concave lenses?

• Virtual and upright.
• Diminished.
• Formed between object and lens.

How are lenses used to form images in the eye?

The lens in our eye refracts light rays to make them converge on the retina where we have specialized cells that can sense light. This lens is constantly adjusting its refracting power so we can see distant and near objects clearly.  When the lenses in our eyes cannot adjust as needed, we can use external lenses - glasses - to help our eyes converge the images.

Where are the images formed in convex lenses?

The location of the image depends on the position of the object:

1. If the object is beyond two focal distances, the image forms between one and two focal distances.
2. If the object is exactly at two focal distances, the image forms at two focal distances, at the other side of the lens.
3. If the object is between one and two focal distances, the image forms beyond two focal distances.
4. If the object is at the focus, the image forms at infinity.
5. If the object is between the focus and the lens, the image forms behind the object.

Where are the images formed in concave lenses?

The image is formed always between the object and the lens.

What is an example of images formed by lens?

A magnifying glass is an example of a convex lens where the image is formed behind the object.

## Test your knowledge with multiple choice flashcards

What would be the image produced if we take a convex lens and see an object at a very far distance?

In which type of lens do the rays of light after refraction converge to a single point?

What will happen to the ray of light that passes through the optical center of a convex lens?

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