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LightRefraction of light
Thin lenses
Description Thin Len Converging Ray Simulation
The Thin lens equation assumed that if the distances from the object to the lens and from the lens to the image are u and v respectively, for a lens of negligible thickness, in air, the distances are related by the thin lens formula:What this means is that, if an object is placed at a distance u along the axis in front of a positive lens of focal length f, a screen placed at a distance v behind the lens will have a sharp image of the object projected onto it.
When Object distance, u is near infinity ( very big compared to f), the lens is used by telescopes. note that Convex (converging) lenses produce an image of an object at infinity at their focus.if the sun is imaged, much of the visible and infrared light incident on the lens is concentrated into the small image. A large lens will create enough intensity to burn a flammable object at the focal point
- When Object distance, u > 2*f, the lens is used by camera when forming images on film and the eyes.
- When Object distance, u = 2*f, the lens is used by photocopier when making equal size copies.
- When Object distance, f < u < 2*f, the lens is used by overhead projector to form magnified image.
- When Object distance, u = f, the lens is used by spotlight when projecting parallel beam of light.
- When Object distance, u < f, the lens is used by magnifying glass when viewing a enlarged image.
where M is the magnification factor; if |M|>1, the image is larger than the object. Notice the sign convention here shows that, if M is negative, as it is for real images, the image is upside-down with respect to the object. For virtual images, M is positive and the image is upright.
Please note that the shape of the lens adjust with the focal length is for illustration purposes, it is not scientific.
This thin lens ray diagram java applet has:
Main view:
Lens that is controllable by the focal length f, +f imply converging lens -f imply diverging lens.Focal points drag-able, 2F, F, F & 2F
u is position of Object from lens center c
v is position of Image from lens center c.
The object is drag-able to the right side of the lens
Top View:
dynamically display a possible use of the lens under different conditions with pictures shared under creative commons licenses and other similar pro usage licenses under attribution.Bottom View:
4 radio buttons: allows for different visualization purposes of light path in the context of lens- no ray
- principal-ray
- marginal ray
- all ray
4 check boxes:
- "Real/Virtual?"
- "Inverted/Upright?"
- "Magnify/Diminish?"
- "Same/Opposite side"
3 slider control:
- u, object distance from c
- h, height of object f,
- focal length of lens
3 values display:
- v,image distance from c
- ih, image height
- M, Magnification
Activity:
Explore the simulation. Notice that you can move the sliders to vary the distance of the object to the center of the thin lens. What do each of the sliders, radio buttons and check-boxes do?Take about 10 minutes to inquiry through the simulation model and describe the action of a thin converging lens on a beam of light. ( this simulation currently does not have beam of light)
Discuss with your lab partner what is the meaning of the focal length f.
hint: in terms of the way the light rays from the object is bend and pass through where?
check the principal rays radio button. Discuss and formulate ideas how the ray diagram allows the drawing of ray diagrams to illustrate the formation of real and virtual images of an object by a
thin converging lens.
- What does the green ray light always do?
- What does the red ray light always do?
- What does the teal ray light always do?
What does the term linear magnification mean in this simulation.
Discuss how it is calculated from?
How many ways are there to determine the magnification of the think converging lens.
Check the no ray radio button. move the sliders a suitable position of your choice. Now, sketch as accurately as possible on a piece of paper, the principal ray diagram ( minimum 2 rays) to get the image position and height. Practice a few times with different and varied examples to allow you to draw scale diagrams to deduce the focal length needed for particular values of magnification (converging lens only)
explore the simulation to make observations of the use of a single converging lens as a
- magnifying glass
- a projector
Suggested answers:
By definition, focal length is the distance between the point in the lens where the light begins to diverge (the nodal point) when the object is set at infinity.Magnification M = - v/u = ih/h
Sample Learning Goals
(i) define the term focal length for a converging lens
(j) draw ray diagrams to illustrate the formation of real and virtual images of an object by a thin converging lens
Version:
Translations
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Credits
Fu-Kwun Hwang; lookang (This email address is being protected from spambots. You need JavaScript enabled to view it.)
Briefing Doc: 🔬Thin Lenses and Their Applications
This briefing doc reviews key concepts related to thin lenses, drawing upon information from the "Thin Converging Diverging Lens Ray Diagram Lens JavaScript HTML5 Applet Simulation Model" hosted by Open Educational Resources / Open Source Physics @ Singapore.
Main Themes:
- Thin Lens Equation: The fundamental relationship governing image formation in thin lenses is 1/u + 1/v = 1/f, where u is object distance, v is image distance, and f is focal length. This equation highlights the interplay between object position, lens properties, and image characteristics.
- Types of Lenses: The resource focuses on both converging (+f) and diverging (-f) lenses, examining how they refract light to form images. Converging lenses are thicker in the center, causing parallel light rays to converge at the focal point. Diverging lenses are thinner in the center, causing parallel light rays to spread outward.
- Image Characteristics: Images formed by lenses can be real or virtual, inverted or upright, magnified or diminished, and located on the same or opposite side of the lens as the object. These characteristics are determined by the object's position relative to the focal length.
- Applications of Thin Lenses: Different object-lens configurations lead to diverse applications, including cameras, telescopes, photocopiers, overhead projectors, spotlights, and magnifying glasses.
Important Ideas and Facts:
- Focal Length: The focal length (f) is a crucial property of a lens, representing the distance at which parallel light rays converge (converging lens) or appear to diverge from (diverging lens). "By definition, focal length is the distance between the point in the lens where the light begins to diverge (the nodal point) when the object is set at infinity."
- Magnification: Magnification (M) describes the size ratio between the image and the object. It is calculated as M = -v/u = ih/h, where ih is image height and h is object height. A negative M indicates an inverted image.
- Ray Diagrams: Understanding ray diagrams is essential for visualizing image formation. Key rays include:
- A ray parallel to the principal axis refracts through the focal point (converging lens) or appears to come from the focal point (diverging lens).
- A ray passing through the center of the lens continues undeviated.
- A ray through the focal point (converging lens) or aiming toward the focal point (diverging lens) emerges parallel to the principal axis.
- Specific Applications: The resource provides examples of how lens properties are exploited in various applications:
- Telescopes: Use converging lenses with objects at near infinity to form images at the focal point.
- Cameras and Eyes: Form real, inverted images on film or the retina when the object distance is greater than twice the focal length (u > 2f).
- Magnifying Glasses: Form virtual, upright, and magnified images when the object is placed within the focal length (u < f).
Quotes:
- "When Object distance, u is near infinity (very big compared to f), the lens is used by telescopes."
- "The magnification of the lens is given by: M = - v/u"
- "By definition, focal length is the distance between the point in the lens where the light begins to diverge (the nodal point) when the object is set at infinity."
Overall, the resource provides a comprehensive overview of thin lens principles and their practical applications. The interactive simulation offers a valuable tool for exploring the relationship between object position, lens properties, and image characteristics.
Thin Converging & Diverging Lens FAQ
1. What is the thin lens equation, and what does it mean?
The thin lens equation is: 1/u + 1/v = 1/f.
This equation relates the object distance (u), image distance (v), and focal length (f) of a thin lens in air. It means that for a given lens with focal length f, if an object is placed at distance u from the lens, a sharp image will be formed at distance v on the other side of the lens.
2. How does the object distance (u) relate to the type of image formed and the applications of the lens?
- u near infinity: Image forms at the focal point, used in telescopes.
- u > 2f: Real, inverted, diminished image, used in cameras and eyes.
- u = 2f: Real, inverted, same-size image, used in photocopiers.
- f < u < 2f: Real, inverted, magnified image, used in overhead projectors.
- u = f: Parallel rays of light emerge, used in spotlights.
- u < f: Virtual, upright, magnified image, used in magnifying glasses.
3. What are principal rays, and how are they used to construct ray diagrams?
Principal rays are three specific rays that follow predictable paths when passing through a lens:
- Ray 1: Parallel to the axis, refracts through the focal point on the other side.
- Ray 2: Passes through the center of the lens without bending.
- Ray 3: Passes through the focal point on the object side, refracts parallel to the axis.
By drawing any two of these rays from a point on the object, their intersection point after passing through the lens locates the corresponding point on the image.
4. What is the meaning of focal length (f) in terms of light ray behavior?
The focal length (f) is the distance from the lens where parallel rays of light converge (for a converging lens) or appear to diverge from (for a diverging lens) after passing through the lens.
5. What is linear magnification, and how is it calculated?
Linear magnification (M) describes how much larger or smaller the image is compared to the object. It is calculated in two ways:
- M = -v/u: Using the image distance (v) and object distance (u). A negative value indicates an inverted image.
- M = ih/h: Using the image height (ih) and object height (h).
6. How does a single converging lens act as a magnifying glass?
When the object is placed within the focal length (u < f) of a converging lens, a virtual, upright, and magnified image is formed on the same side as the object. This principle is used in magnifying glasses, where the lens allows us to see an enlarged view of a nearby object.
7. How does a single converging lens act as a projector?
When an object is placed beyond the focal length but within twice the focal length (f < u < 2f) of a converging lens, a real, inverted, and magnified image is formed on the other side of the lens. This is the principle used in projectors, where a bright light source illuminates a slide or transparency, and the lens projects a magnified image onto a screen.
Google Play Store Apps
https://itunes.apple.com/us/app/lens-converging-diverging/id1164800839?mt=8
ICT connection lesson
- http://library.opal.moe.edu.sg/ictc&func=view&rid=2047 by Joseph Chua
Learning Outcomes
- Describe (to tell or depict) how light behaves when it passes through a thin converging or diverging lens.
- Define (to state the meaning) the term focal length for a thin converging lens.
- Draw (to sketch accurately) ray diagrams to illustrate how real and virtual images are formed by a thin converging lens.
Video
Ejs open source converging & diverging Lens object image high school java applet by Loo Kang Wee
https://notebooklm.google.com/notebook/31dba337-8493-47c0-ad9a-73cbc0228fb4/audio
ICT connection lessons
- http://library.opal.moe.edu.sg/ictc&func=view&rid=2047 by Joseph Chua
Version:
- http://weelookang.blogspot.sg/2015/05/ejss-thin-converging-diverging-lens-ray.html Blog Post JavaScript version by Fu-Kwun Hwang and Loo Kang Wee
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1155.0 Ejs open source converging & diverging Lens object image high school java applet by Fu-Kwun Hwang and Loo Kang Wee
- http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=704.0 Relation 1/p+1/q=1/f Java Version by Fu-Kwun Hwang
Other Resources
- http://physics.bu.edu/~duffy/HTML5/Mirrors.htmlby Andrew Duffy
- http://physics.bu.edu/~duffy/HTML5/Lenses.html by Andrew Duffy
- https://www.geogebra.org/m/BRzg3uZ6 Reflection and Refraction by ukukuku
- https://www.geogebra.org/m/a2rNFfHA Lens Refraction and Spherical Aberration by ukukuku
- https://evantoh23.wordpress.com/2020/08/01/not-just-the-3-rays/#respond nice drawing by evan toh
- https://www.geogebra.org/m/N8cCAwne Tom Walsh
- https://cosci.tw/mobile/?name=NZR8s61534208656624 by cosci https://youtu.be/Ag7SvMiZqF4
FAQ
Thin Converging & Diverging Lens FAQ
1. What is the thin lens equation, and what does it mean?
The thin lens equation is: 1/u + 1/v = 1/f.
This equation relates the object distance (u), image distance (v), and focal length (f) of a thin lens in air. It means that for a given lens with focal length f, if an object is placed at distance u from the lens, a sharp image will be formed at distance v on the other side of the lens.
2. How does the object distance (u) relate to the type of image formed and the applications of the lens?
- u near infinity: Image forms at the focal point, used in telescopes.
- u > 2f: Real, inverted, diminished image, used in cameras and eyes.
- u = 2f: Real, inverted, same-size image, used in photocopiers.
- f < u < 2f: Real, inverted, magnified image, used in overhead projectors.
- u = f: Parallel rays of light emerge, used in spotlights.
- u < f: Virtual, upright, magnified image, used in magnifying glasses.
3. What are principal rays, and how are they used to construct ray diagrams?
Principal rays are three specific rays that follow predictable paths when passing through a lens:
- Ray 1: Parallel to the axis, refracts through the focal point on the other side.
- Ray 2: Passes through the center of the lens without bending.
- Ray 3: Passes through the focal point on the object side, refracts parallel to the axis.
By drawing any two of these rays from a point on the object, their intersection point after passing through the lens locates the corresponding point on the image.
4. What is the meaning of focal length (f) in terms of light ray behavior?
The focal length (f) is the distance from the lens where parallel rays of light converge (for a converging lens) or appear to diverge from (for a diverging lens) after passing through the lens.
5. What is linear magnification, and how is it calculated?
Linear magnification (M) describes how much larger or smaller the image is compared to the object. It is calculated in two ways:
- M = -v/u: Using the image distance (v) and object distance (u). A negative value indicates an inverted image.
- M = ih/h: Using the image height (ih) and object height (h).
6. How does a single converging lens act as a magnifying glass?
When the object is placed within the focal length (u < f) of a converging lens, a virtual, upright, and magnified image is formed on the same side as the object. This principle is used in magnifying glasses, where the lens allows us to see an enlarged view of a nearby object.
7. How does a single converging lens act as a projector?
When an object is placed beyond the focal length but within twice the focal length (f < u < 2f) of a converging lens, a real, inverted, and magnified image is formed on the other side of the lens. This is the principle used in projectors, where a bright light source illuminates a slide or transparency, and the lens projects a magnified image onto a screen.