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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Jetzt kostenlos anmeldenHave 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.
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.
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.
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.
We can classify the images formed by lenses as real or virtual.
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.
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.
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.
Since the magnification is a ratio it has no units.
Consider an object tall. If a lens produces an image with a height of, calculate the magnification.
The magnification of the image is, which means it is four times larger than the object.
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.
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.
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 asand.
In general, a convergent lens is thicker in the middle.
The behaviour of the light rays that go through a convex lens can be summarized as three basic rules.
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,. We can distinguish five cases:
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.
In this case, the image is:
This is the same example of image formation as in the photo showing the image of a house at the beginning of the article!
Let's repeat the same procedure. For this case, the image is:
Under these conditions, the image is:
This case is peculiar. The light rays are parallel after refracting and never intersect. Therefore, we say the image forms at infinity.
The image formed will be:
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.
In this case, the image produced will be:
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!
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.
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.
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.
The following ray diagram represents the same situation.
In general, a divergent lens is thicker on its edges.
We can summarize the behavior of light rays as going through concave lenses as three rules.
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.
The image formed by the concave lens is:
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.
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.
We can correct this using concave lenses. These lenses disperse the light rays so that the eyes can converge the light at the retina.
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,
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.
The location of the image depends on the position of the object:
The image is formed always between the object and the lens.
A magnifying glass is an example of a convex lens where the image is formed behind the object.
What would be the image produced if we take a convex lens and see an object at a very far distance?
Diminished and inverted.
In which type of lens do the rays of light after refraction converge to a single point?
Convex lens.
What will happen to the ray of light that passes through the optical center of a convex lens?
It will move without any deviation.
An imaginary vertical line that goes straight through the optical center is called:
Principal axis.
What will happen to a ray of light parallel to the principal axis after refracting from a convex lens?
It will pass through the focal point.
In which direction will the ray of light be refracted if it passes through the principal focus of a convex lens?
It will move parallel to the principal axis after refraction.
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