Image Formation by Lenses
Check out the pics below! They're of two different images seen through a lens. The one on the left is of a tiny house that looks upside down and smaller. On the other hand, the snap on the right is of a postage stamp that appears bigger and right side up. It's pretty amazing that both images are through the same lens, right? You can also try this yourself with a magnifying glass. Just move it closer or further away, and watch how the picture changes. Cool, huh? This is all part of understanding how lenses form images.
Are you curious about why images appear differently through lenses? We've got you covered! In this article, we'll discuss the different types of lenses and how their shapes affect the way light passes through them. We'll also share some simple rules that explain how light behaves when passing through lenses. By understanding these rules, you'll be able to predict the size, orientation, and magnification of any image formed through a lens. So, get ready to dive into the fascinating world of lens image formation!
How does an image form when using lenses?
Lenses work by using the refraction of light.
Refraction is the change in the direction of light when changing from one medium to another due to light propagating at different speeds on them.
Light propagates faster in the air than it does in water. Therefore, when the light goes through the water-air interface, it changes its direction. This is why an object looks like it is bent when it is partially submerged in a glass of water. The light coming from the submerged part seems to come from a different position than it really is.
Types of images formed by lenses
We can classify the images formed by lenses as real or virtual.
Lenses can form two types of images: real and virtual. Real images are formed when light rays converge or diverge from a source and can be projected onto a screen. For example, a spherical concave mirror can produce a real image that is inverted. By placing a paper at the point where the image forms, the picture can be projected onto the paper sheet. On the other hand, virtual images are those that appear to come from a source that is not there, and cannot be projected onto a screen. Plain mirrors produce virtual images, and the image appears to be behind the mirror. Images can be upright or inverted, enlarged, diminished or unchanged in size. Magnification is a measure of the size of the image compared to the object. It is calculated by comparing the height of the object to the height of the image formed by the lens. The magnification is a ratio with no units, and can be used to determine the size of the image formed by the lens.
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 center of a lens.
We can distinguish a convex lens by its curved or rounded outwards shape.
Note that light refracts two times, as mentioned before. Since the lens can be used in both directions, it has two foci. Both are at the same distance from the lens's geometrical centre - also called the optical centre - and both lie on the principal axis. The distance from the lens centre to its focus is called focal distance.
We can use ray diagrams to understand how a convex lens forms an image. In a ray diagram, we consider that light rays only refract at one point, and we use a simpler representation for the converging lens. Below is a diagram representing the same picture of the convex lens shown before.
Note that we have labelled the foci to distinguish them. The focus, on the left-hand side of the lens, is and the focus on the right-hand side of the lens is . It is important to mention that, in general, a lens will be convergent if it is thicker in the middle.
Rules for image formation by convex lenses
Understanding the behaviour of light rays passing through a convex lens is essential to understanding image formation. There are three basic rules that summarize the behaviour of light rays through a convex lens. First, a light ray that is parallel to the principal axis passes through the focus on the other side of the lens after refraction. Second, a light ray that passes through the optical centre of the lens does not change direction. Finally, a light ray that goes through the focus moves parallel to the principal axis after refraction. By applying these rules, we can predict how light rays will behave as they pass through a convex lens, and use this knowledge to understand how images are formed.
The principle of reversibility of light states that light follows the same path if the direction of a light ray is reversed. This principle explains why the first and the second rules are opposite each other. We can identify where the image of an object will form by tracing the light that comes from a specific part of the object. It is enough to draw two light rays from the top of the object and see where these rays meet. The point of intersection locates at the top of the image.
Examples of image formation by convex lenses
When using a convex lens, the resulting image depends on the distance of the object from the lens. There are five special cases that can be distinguished based on the object's distance:
- If the object is beyond two focal distances, then the image will be real, inverted and diminished in size.
- If the object is exactly at two focal distances, then the image will be real, inverted and the same size as the object.
- If the object is between one and two focal distances, then the image will be real, inverted and enlarged in size.
- If the object is at the focus then there will be no image formed as the light rays will be parallel.
- If the object is between the focus and the lens, then the image will be virtual, upright and enlarged in size.
Understanding these special cases is important in predicting the type and characteristics of the image formed by a convex lens, and can be helpful in various practical applications.
Case 1: Object placed beyond two focal distances
For this case, the object is placed beyond two times the focal distance. We need to draw two rays coming from the top of the object to see where they meet. For example, we can use rules 1 and 3. Therefore, one of the rays passes through the optical centre without deviation. And the other travels parallel to the principal axis, refracting and passing through the focus.
As we can see, if the object is beyond two focal distances from the lens, the image formed is: Real Diminished Inverted Formed beyond the focus but before two focal distances. This is the same situation 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
For this case, the object is placed at exactly two focal distances.
To correct farsightedness, convex lenses are used. These lenses are thicker at the edges and thinner in the middle, causing light rays passing through them to converge towards the focal point. When a person with farsightedness wears a convex lens, the light entering their eyes is refracted in such a way that it converges towards the retina, allowing them to see nearby objects clearly.
The amount of correction required for farsightedness depends on the severity of the condition. A person with mild farsightedness may only need a low-power convex lens, while someone with severe farsightedness may require a high-power convex lens.
It's important to note that while convex lenses can correct farsightedness, they cannot cure the underlying condition. Therefore, people with farsightedness may need to wear glasses or contact lenses for the rest of their lives.
In conclusion, convex lenses are a powerful tool for correcting farsightedness and have been used for centuries to help people see more clearly. By understanding how these lenses work and the different scenarios in which they can be used, we can appreciate their importance in our daily lives.
This condition can be corrected by using a converging lens. A convex lens can help the lens-cornea system to converge the light rays at a shorter distance, allowing them to converge and focus on the retina.
Image formation by concave lenses
A concave lens or diverging lens causes the light rays parallel to the principal axis to disperse after refraction, spreading out so that it looks as if they are all emerging from one point called the principal focus of the lens.
Concave lenses can be distinguished by being hollowed out or rounded inwards. The following image illustrates how light rays passing through a concave lens disperse.
Similarly, as with convex lenses, light refracts twice, but we can simplify the situation and create a ray diagram. The following ray diagram represents the same situation shown in the previous picture.
Note that, in general, a lens will be divergent if it is thicker on its edges.
Rules for Image formation by concave lenses
We can summarize the behavior of light rays as going through concave lenses as three rules.
A light ray after diverging will appear to come from the focus if it is parallel to the principal axis before refracting. A ray of light will go through the optical center without any deviation. A ray of light going towards the principal focus will refract and afterward will move parallel to the principal axis.
Once more, notice that the first and third rules are related to each other.
Example of image formation by concave lenses
Let's have a look at the picture below. An object is placed beyond the focal distance but no farther than two focal distances. Applying the first rule, we know that a light ray from the top of the image that moves parallel to the principal axis diverges after refraction. On the other hand, a light ray going through the optical centre will move without deviation. The image formation for this scenario is shown in the below figure.
The properties of the image in this scenario are:
Virtual and upright Diminished Formed between the object and the lens
For a concave lens, the object's position does not matter, as the properties of the image formed will be the same for all positions.
Correcting nearsightedness with concave lenses
Nearsightedness or myopia is a condition where a person can clearly see near objects, but not distant ones.
The lens-retina system, for a person with nearsightedness, converges the light rays in front of the retina, resulting in a blurry image.
We can correct this by using concave lenses. The lenses disperse the light rays so that the cornea-lens system can make the rays converge at the retina.
summary, understanding the key takeaways of image formation by lenses is crucial in comprehending how lenses work and their applications. Convex lenses are converging lenses that curve outwards, while concave lenses are diverging lenses that curve inwards.
For convex lenses, there are three key rules to remember: a light ray parallel to the principal axis will pass through the focus on the other side of the lens, a light ray passing through the focus will move parallel to the principal axis after refraction, and a light ray passing through the optical centre will not be deflected.
The image formation for convex lenses has five different cases depending on the object's placement on the principal axis, which can result in real or virtual images that are either upright or inverted, enlarged or diminished.
Concave lenses, on the other hand, only produce virtual and upright images that form between the object and the lens, regardless of the object's position.
Convex lenses are used to correct farsightedness or hyperopia, while concave lenses are used to correct nearsightedness or myopia. By using the appropriate lenses, people with these conditions can see objects clearly at different distances.
Overall, understanding the properties and applications of lenses is important in fields such as optics, ophthalmology, and photography, among others.
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: If the object is beyond two focal distances, the image forms between one and two focal distances. If the object is exactly at two focal distances, the image forms at two focal distances, at the other side of the lens. If the object is between one and two focal distances, the image forms beyond two focal distances. If the object is at the focus, the image forms at infinity. 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.
