Lab Report: Finding a Focal Length of a Convex Lens

relationship between the convex lens and the focal point

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Physics: optics of lenses and mirrors (11)

Physics: Introduction to the optics of lenses and mirrors. Concave, convex, converging, diverging; real, virtual; upright, inverted, magnified, shrunk. Sign conventions for focal length, image distance, object distance, magnification. The lens/mirror equation; the magnification equation. Introduction to ray tracing. This is arecording of a tutoring session, posted with the student's permission. These videos are offered on a "pay-what-you-like" basis. You can pay for the use of the videos at my website: www.freelance-teacher.com For printable documents containing the "handout" and problems discussed in this video series, go to my website. For a list of all the available video series, arranged in suggested viewing order, go to my website. For a playlist containing all the videos in this series, click here: www.youtube.com (1) The lens/mirror equation. Focal length distance, object distance. Convex, concave, diverging, converging (2) Image distance. Real, virtual (3) Continued (4) Continued. Upright, inverted (5) Continued. Magnification equation (6) Continued. The lens/mirror chart (7) A problem (8) Continued. Ray tracing (9) Continued (10) Another problem (11) Continued

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Sunlight Solar Panel - Diffused Sunlight Solar Panels Get the Most From a Small Space

There are many ways to capture the warmth, light and energy from the sun. One of the newest ways is something called a conical diffused sunlight solar panel. These panels take a small area of sunlight and concentrate it into a narrow beam to be used as heat. Early forms of this type of solar panel were used as skylights, creating a "light" by using a mirror lined tube that extends to the roof, capturing the sunlight and transferring it to a translucent plate or dome which glows from the captured light. While effective at creating light in areas with no windows, all the heat from the sunlight is lost in the process.

A conical diffused sunlight solar panel takes this process of transferred sunlight from one area to another a few steps further. By taking a convex lens mounted on the roof, a narrow circular beam of light can be transferred through a series of lenses and concentrators creating a convergent lateral beam of light. This will eventually be focused on a heat duct and generate a great deal of energy. The transferred heat can then be piped to other parts of the building. The actual process is a lot more complex, but basically a conical diffused sunlight solar panel takes a small area of sunlight to generate a great deal of heat.

These conical diffused sunlight solar panels use a complex process to transfer sunlight into energy, but they are very effective. They are utilizing a small area of available sunlight, concentrating the beam to ostensibly magnify the sunlight into a compact unit. This is rather like taking a magnifying glass and focusing it to create a pinpoint of very hot energy. Large buildings with little sunlit surface can still get an effective heat source using the sun's energy this way. Although the process is fairly technical in design, there are potentially a lot fewer things which can go wrong with this type of solar energy as opposed to active electric producing solar panels.

This type of solar energy is particularly effective with larger structures because the heat generated is intense and installation is a multifaceted matter. New designs of conical diffused sunlight solar energy panels are in development and may soon be easily usable for any situation, particularly those with limited access to sunlight. Other forms of solar panels are looking at implementing this design as well simply because it is so efficient.

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Physics:Converging lenses

See how converging lenses affect the path of light.=)

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Concave lens - physics experiment

www.fizik.si Lens that possesses at least one surface that curves inwards. It is a diverging lens, spreading out those light rays that have been refracted through it. A concave lens is thinner at its centre than at its edges, and is used to correct short-sightedness (myopia).

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The Physics Of Contact Lenses

Contact lenses are used for vision correction and are placed on the cornea of the eye. They do the same corrective function that conventional spectacles, or glasses, do. However, in comparison, they are very light in weight and are, for all purposes, invisible. Contact lenses help form the image on the retina of the eye by either converging or diverging the rays of light entering the eye.

Earlier contact lenses were made of glass, and were scleral lenses. Scleral lenses are large contact lenses that cover the complete sclera - the white outer coating - of the eye. These unwieldy lenses could only be worn for a short period at a time. With the development of PPMA - polymethyl methacrylate - in the 1930s, plastics were first used in contact lenses. These were in fact, hybrid scleral lenses, made with the combination of both, glass and plastic, in 1936.

By the 1950s, much smaller contact lenses were developed that covered only the cornea of the eye and not the whole eye.

Types of Vision Impairments
One of the major uses of contact lenses is to correct visual defects. The general impairments are Myopia, Hyperopia, Astigmatism, and Presbyopia.

Myopia - is a visual disability where the image of the object seen is formed in front of the retina. During this visual impairment, one can see objects that are near, and not the distant objects, which appear blurred. This defect is also known as nearsightedness. This is a very common impairment, with over 25 percent of the adults in the United States suffering from it. The defect can be corrected by the use of concave contact lenses.
Hyperopia - It is also known as Hypermetropia, and the image of the object is formed behind the retina. Far objects can be seen clearly, and the near objects appear to be blurred. Hyperopia is more commonly known as farsightedness, and more than 13 percent of the children in the United States, in the age group 5 to 17, suffer from it. The defect can be corrected by the use of convex contact lenses.
Astigmatism - This happens when the lens of the eye has more than one focal point, in different meridians. Astigmatic people cannot see in fine detail, and need cylindrical lenses to correct their impairment. Nearly 34 percent of American children in the age group 5 to 17 have this impairment.
Presbyopia - This is an impairment, which comes with age, generally after the age of 40. The impairment develops as the lens of the eye loses its elasticity. Bifocal contact lenses are used to correct this vision defect.

Lenses Used For Vision Correction
In the case of normal vision, the light from the object hits the cornea and focuses on the retina. Due to some refractive error, at times the light from the object does not focus on the retina, but either in front of it, or behind it. To correct this refractive error, contact lenses are used to focus on to the retina.

The type of contact lenses used depends on the type of vision impairment, and how much refractive error is involved. How much the lens bends the light to focus on the retina is measured in diopters (D).

Myopia occurs when the light is focused in front of the retina, as the eyeball is longer than normal. To correct this impairment, which is also known as nearsightedness, a concave lens is used. This lens is thinner at the center, and helps move the focus ahead, towards the retina.

To correct this vision impairment, the curvature in the concave contact lenses is determined by the measurement in diopters. The larger the number of diopters, larger is the vision defect. In myopia, the diopter number is preceded by a minus (-) sign, denoting that the focus is short of the retina.

In the case of hyperopia, the light is focused beyond the retina. Hyperopia is also known as farsightedness, as distant objects are seen clearly in this impairment. The eyeball is shorter than normal, and a convex lens is used to correct this vision defect. The contact lens used is thicker in the center, and helps move the focus back onto the retina.

In this case, too, the curvature required in the convex contact lenses is determined by the measurement in diopters. The diopter number is preceded by the plus (+) sign, denoting that the focus is beyond the retina.

The lenses used for the correction of myopia and hyperopia are categorized as spherical contact lenses.

When the cornea is irregularly shaped, the light from the object falling on the cornea focuses on more than one point. This distortion of the image is called astigmatism. Special lenses need to be designed, based on the individual's distortion of image. These lenses are known as toric lenses.

Though toric lenses are made of the same materials as the spherical lenses, they are specifically designed to suit individual impairments. These lenses have different curvatures, thicker in some places, and thinner in others. These lenses are designed to correct astigmatism and myopia or hyperopia, if required.

For the correction of presbyopia, special bifocal lenses are required, as the person suffering from it requires both correction for nearsightedness and farsightedness. In such lenses, either the correction for near impairment is placed in the center of the lens, with the distant correction on the outside, or vice versa.

Types Of Contact Lenses
The initial lenses were rigid lenses that did not absorb water. This kept the oxygen from passing into the cornea of the eye, causing eye irritation and other discomforts.

Then came the soft contact lenses made from hydrogel, which allowed oxygen to pass through them to the cornea. These lenses came to be known as 'breathable' contact lenses. This made it possible for contact lenses to be worn comfortably and for longer periods. Today, there are:

Daily wear lenses, which are removed at night.
Extended wear lenses that can be worn for extended periods without removing.
Disposable lenses that can be discarded after a day, a week, or a few weeks.

In addition, there are color contacts, which are for cosmetic purpose.

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How to Use a Telescope - Galileo's First Telescope and Its History

Galileo Galilee is known as the "father of telescopes" and rightly so. He is the inventor of the telescope and every telescope made after his invention follows the same principle that he used. Galileo's telescope was a primitive prototype of the telescopes that are used widely today. However, the principles he used are the very same ones still being used to this day. Galileo's telescope used two lenses - one concave and one convex - inside a tube-light shaped device. Convex lenses are those lenses whose edges curve inwards and concave lenses are lenses that have outward curves at the edge. The eyepiece in the telescope was constructed with the concave lens. Spy glasses, invented around the same time and used by militants to observe enemy activity in camps, were a major inspiration to Galileo in making his own telescope.

When two lenses are combined together, they are able to collect more light than individual lenses. This is the main principle behind Galileo's telescope. Most of the telescopes in use today, use the same principle. The human eye also works on a similar principle, but cannot collect too much light. Telescopes are able to gather more light because of the double lenses used in its construction. These lenses gather light and build an image by focusing the light at a point. Refraction is the mechanism in use to form such images. As a result, telescopes are also called refracting telescopes or refractors. The phenomenon by which the collected light bends and forms images is known as refraction.

Images were magnified by a factor of 30 in Galileo's invention. However, the shape of the lenses he used was such that his image became blurred and distorted. But no one had ever invented something so exciting with which to observe the night skies before Galileo's telescope. Galileo used his telescope to view the moon and observe it closely. He was also the one to figure out that the magnification factor of a telescope was provided by the ratio of the power of the concave lens to the power of the convex lens. So he premised that the simplest way to increase this magnification factor was to use a high power concave lens with a weaker convex lens.

In Galileo's time, there were only low strength lenses available. Due to this restriction, Galileo decided to make his own lenses. He was soon able to achieve a magnification of 9x with lenses hat he had ground himself. His telescope was fitted with his own lenses. It was just another feather in his already well-decorated cap.

As time passed, Galileo improvised on his primitive telescope, making several modifications to it. He also demonstrated his invention at the Senate of Venice, and several senators climbed the highest towers of the time to observe the horizon with Galileo's invention. They viewed the distant ships from their perches and decided that the telescope was a very useful military device.

The telescope changed the face of Astronomy and became an indispensable part of the study. Several inventors used the same principle and made telescopes of their own. Gradually over the years, the study of astronomy benefited immensely from the telescope and its uses. The same principle was employed in the construction of much more powerful telescopes that made it possible to understand our plane and its surroundings more comprehensively, all thanks to Galileo's wonderful invention.

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The Most Powerful Telescope Will Fit Into Your Pocket

Shrinking the Telescope - "Astronomers in the last 50 years have made wondrous discoveries, expanded our understanding of the universe and opened humanity's vision beyond the visible portion of the electromagnetic spectrum. Our knowledge of how the cosmos was born and how many of its phenomena arise has grown exponentially in just one human lifetime. In spite of these great strides there remain fundamental questions that are largely unanswered. To further our understanding of the way our present universe formed following the Big Bang requires a new type of Observatory having capabilities currently unavailable in either existing ground-based or space telescopes."

The bigger is better concept is so embodied within our consciousness, that just the idea of smaller more efficient telescope seems to defy all the laws of science. Yet, science always supports Miniature Size Telescopes. It is, however, the lock of understanding of the fundamental principle of focus that has deprives us over the centuries. Research in this field has provided a full understanding of the science behind optical telescope operation that has contributed to the design of the next generation of telescopes. The introduction size of miniature telescope will be the size of a viewfinder now used on present telescopes. Yet, these new generation of telescopes will posses resolving powerful greater than even the largest known telescope.

Technique in lens and mirror manufacturing has improved significantly over the centuries. With the aid of computers, lasers, and robotics technologies, optics can be made with precision accuracy. Eventually, the size of telescopes will reduce to wearable instrument as small as a pair of eyeglasses, in the not so distance future. Telescopes will soon be comprised of very small (a few centimeters in length) tubes fitted into a headgear. They will have the advantage of precise movement and shock absorbent the human head provides. Wide field of view similar to that of the naked eye, impressive focus, infinite magnification (limited only by light pollution and disturbance), and brightness allowing snap shot color photographing and live video recording. Headgear will be convenient, efficient, and versatile. The design reserves the potential to be up-graded and customized. After almost 400 years of telescope development, we finally have a revolutionary breakthrough now capable of reshaping telescopes science and create revolutionary optical devices to shrink football size telescopes to a view finder, and eventually into a pair of glasses. Welcome to the new age of telescope technology.

The Impossible Made Possible - As our technological achievements shape the future, we find ways to make the impossible possible. We constantly improve existing technology by making them smaller and more efficient. In many cases, smaller more integrated designs increase the wide category of efficiencies. We are now capable of manufacturing instruments on a microscopic scale, with the exception of the optical telescope. Optical telescope is the only instrument that actually grows in size rather then shrink. As we advance in research and development of these instruments, they grow larger in size with each new generation. It is every astronomer dream to have access to a high resolving power telescope, yet small enough to be portable.

However, it is embedded in our minds that we are unable to increase resolution with reduced size in a single design. In relation to this, engineers continue to build bigger and bigger instruments, creating monsters and giants. The reason Miniature Size Telescope is considered impossible lies not only with optical science, but also with unclear understanding of the principle of light. We still don't understand the complex interaction involved in both viewing and capturing images, until now. It is for this uncertainty, why we still use two different theories of light. Light is viewed as a particle that accelerates from point A to point B, and light is also viewed as waves that transmit by means of wave motion. Where one theory fails to make sense, the other is applied. Miniature Size Telescope is base on 'Unify Theory of Light'.

The Science - Our eyes are very unique: a young person's pupil dilates between 2 and 7 millimeters, yet, the eye posses the ability to view images several thousands meters in diameter. Our wide field of view provides convincing evidence that we view converging image rays and not parallel rays. Converging image rays obeys the inverse square law of electromagnetic radiation. Converging rays describe rays that convert towards a point. Therefore, image carried by these rays reduce their cross sectional area with distance travel. Images collected by the largest telescope aperture, actually enters the few millimeters of our eyes. Small sight angle (true field) at seconds of a degree, so small the brain finds it difficult to isolate the details they contain for recognition, when they are factored into our full field of view. These small-angles of information get compressed within our large field of view, and appear to be just a small spot or become invisible.

Nevertheless, magnification provides the means by which small sight angles are converted into larger ones. A refractor telescope with an aperture of 30 millimeters and 120 millimeters focal length (focal ratio f/4), providing a magnifying power of 5x times and will have an exit pupil of 5 millimeters. This is a very bright telescope, tapping close the maximum of 7 millimeters opening of the pupil. If a second telescope was constructed, having identical aperture size of 30 millimeters, but have a focal length of 1200 millimeters (f/40). The magnifying power will be 50x times. Instead of a 5 millimeters exit pupil, such telescope will now have an exit pupil of only 0.5 millimeter. From the same formula, to obtain a 50x times magnifying power and an exit pupil of 5 millimeters, the aperture needed is 300 millimeters.

Refractor telescopes cannot obtain a 7 millimeters exit pupil without being affected by aberrations. In order to overcome this, telescope designers attempt to allocate a balance between magnification and brightness. Resolving power describes this balance. The compromise will reduce brightness, but increase magnification power and image clarity by the same proportion. The ocular plays an important role in finalizing the image of the apparent field. They are capable of influencing field of view, magnification, and exit pupil (brightness). A short focal length ocular will provide a large magnifying power, small field of view, and short exit pupil; while, a long focal length ocular will provide a small magnifying power, large field of view, and long exit pupil. From this example, one can see that magnification is inversely proportional the diameter of the exit pupil, and exit pupil is directly proportional to brightness.

From the bigger is better formula, we know that by increasing the aperture of the objective, we can increase the exit pupil and thus the brightness of the image. There are several optical design aberrations that set restriction on modem telescope design. In designing optical systems, the optical engineer must make tradeoffs in controlling aberrations to achieve the desired result. Aberrations are any errors that result in the imperfection of an image. Such errors can result from design or fabrication or both.

Achromatic lenses are developed to reduce color aberration created whenever white light is refracted, but with even the best designs, color aberration cannot be totally eliminated. Color aberration also consists of a secondary effect called the secondary spectrum. The longer the focal ratio, the fainter the secondary spectrum becomes. Color aberration limits most refractors to a focal ratio of f/15. Reflectors, which is less affected by color aberration, has focal ration of f/5 for commercial design and f/2.5 for professional designs. Within known telescope design, the different conditions necessary for image perfection is integrated, thus forcing engineers to compromise to obtain a close balance that will render the best possible image.

What if magnification, focus, and brightness could be separated? The new formula for âEUR~Miniature Size Telescopes' isolates each of these factors and allow each to be independently tuned for maximum efficiency.

The Desire for Magnifying Power- "The Overwhelmingly Large Telescope (Owl) is an awesome project, which requires international effort. This huge telescope main mirror would be more than 100 meters in diameters and will have resolution 40 times better than the Hubble Space Telescope. This is a telescope with a primary mirror the size of a foot ball field."

The need for greater magnifying power started with the Galilean design. Research and experiments to improve the telescope's magnification shows that increase in magnification power is directly proportional to the difference in the focal length of the objective and the ocular (eyepiece), where the ocular focal length is the shorter of the two. The race to build the most powerful telescope started at an early age in telescope development. The greatest minds at the time compete to dominate the shaping of this new technology.

During this era, telescope tubes were made very long. At times, these tubes reach length that renders them unstable. In some cases the tubes were removed from the instrument's design. Tubeless telescopes were called aerial telescopes. As telescope Engineers compete to develop more powerful telescopes, they unknowingly encountered a secondary problem that limits the length and magnification of these early 'refractor' telescope designs. They notice that images became darken with increase magnification. Some how, magnification was reducing the amount of light entering and or exiting the telescope lenses. The explanation for this phenomenon, was that enough light wasn't exiting the telescope's ocular, as enough light wasn't been collected at the objective. An increase in the aperture size increases the exit pupil and the problem of dark image with magnification was solved.

At this stage in telescope development, only Keplerian and Galilean 'refractor' telescopes were invented. Lens making was in its early stages and it was difficult to manufacture quality lenses. Large aperture lenses were even a bigger challenge. Refractor telescope soon reach its' size limitation, but now that the second section to the formula for high resolving power is known, reflector telescope of several variations was born.

To date, almost 400 years later, the same formula is still used. Modem improvements simply increase the quality of the optics now use, where modification minimized aberrations. We can now build larger telescopes with resolving power and brightness never taught possible in the time of Galileo, but the formula used in developing these modem instruments is the same as the earliest designs-bigger is better. The bigger is better formula is not without limitations. For example, color aberration limits the brightness of a refractor telescope, which requires a focal ratio of f/I 5 to filter out secondary spectrum aberration. The required focal ratio limits the light collecting capabilities of refractors. Reflectors are not affected by secondary spectrum effect. Focal ratio in the range of ff2.5 is reasonable when requiring exit pupil close to 7 millimeters. However, any attempt to increase magnification within these reflector telescopes while maintaining brightness, will require increase in the aperture and the focal length in the same proportion. It is these design features that makes the phrase âEUR~bigger is better' so convincing.

Previous Limitations - Understanding of the principle of light has rewarded us with the development of modern optical technology. The present article is written to introduce a breakthrough in research and development of Small Powerful Telescopes. Most major telescope manufactures will inform you that magnification is not of significant importance; and that brightness is a more pronounce concern a buyer should have when shopping for a telescope. Magnification and brightness are equally important for viewing and capturing distant images, but the most important factor in rendering details in an image, is focus. Of all the fundamental principles involve in capturing an image, focus is less understood. The awareness of an image focal point and how to achieve a focus image can be easily calculated, but what are the electrodynamics interactions that composed a focus image is still unanswered.

All optical instruments are design around focus; therefore it will always be a top priority in the formation of clear image. Magnification and brightness are of secondary importance, they are the result after focus is achieved. It is the critical distance of focus that determine the maximum magnification and brightness at which an image will be clearly viewed. Magnification describes the action of converting smaller sight angles (true field) into larger ones (apparent field), this provide change in the angle at which the image rays are received, thus, tricking the brain into believing that the object is either closer or larger then it really is. If it wasn't for the need for focus, a single convex lens âEUR"a magnifier-would be a telescope capable of infinite zoom magnification, through the action of simply varying the distance it is held from the eye. Unfortunately, however, there is a critical distant at which images are focus through a single lens or even a system of lenses. This is also known as the critical distance of focus.

What is focus? Webster's Dictionary: fo-cus; is the distinctness or clarity with which an optical system renders an image.

Four Hundred Years History - The discovery of distant magnification was by accident. Early lens maker, Jan Lippershey was experimenting with two different lenses when he discovered the effect of distant magnification. He found that by holding a negative lens close to the eye while holding a positive lens in alignment with the first, away from the eye, that distant objects appeared much closer than they would with the naked eye. Since then, research to understand and explain the science behind these magical devices is still being attempted. Even with today's technology, telescope designers are still faced with major design limitations and challenges that forge a compromise between telescope size, brightness, and image clarity. Scientists have always been puzzled by the nature of light. Sir Isaac Newton regards light as stream of tiny particles traveling in straight line. Dutch scientist Christian Huygens, on the other hand, believed that light consisted of waves in a substance called the ether, which he supposed fill space, including a vacuum. Huygens concept became accepted as the better theory of the two. Today, however, scientists believe that light consist of a stream of tiny wave pockets of energy called photons.

The Bigger is Better Formula - "With a telescope that has 10 times the collecting area of every telescope ever built. You would be able to go down several thousand times fainter than the faintest thing you see with todayâEUR~s telescopes."

The formula that shaped known telescopes over the centuries of development is pretty basic, well known, and proven- bigger is better. This is the same as saying that larger aperture provides brighter image, while longer focal length provides greater magnification. Even so, is this formula written in stone? Let's put the formula to the test. Can large magnification be obtained without long focal length objective? The answer is yes. Microscopes provide very large magnification with relatively short focal length objective. Is it possible to collect light without very large aperture size? Again, the answer is yes. Microscope also demonstrates this. Then why is it that microscopes provide great magnification with adequate brightness at a relatively small size, while telescopes cannot? This shows that it isn't the law of magnification nor brightness, but it the instrument's design limitations that insist on the concept that bigger is better. A basic Keplerian design telescope operates as a microscope when viewed through the other end of the tube. From the fact that telescopes are basically an inverted microscope, one can see the close relationship between the two.

An international standard full size student microscope provides as much as 400x magnifying power, yet such a microscope consists of a tube less then 20 centimeter in length. Sufficient light is reflected from its' plain-o-convex mirror less than 7 centimeters in diameter. In order to obtain identical brightness and magnifying power in a telescope, focal ratio of f/2.5 is recommended for an exit pupil close to 7 millimeters. Such telescope will require an aperture of 320 centimeters (3.2 meters) and a focal length of 800 centimeters (8 meters), calculating roughly with a 20 millimeters ocular. This is an increase of almost 50x in size. This shows that brightness is not limited to large aperture, nor magnification limited to long focal length. However, the 'bigger is better' formula is a design limitation that surface only in distant magnification. Focusing of distant images is more challenging than focusing of close-up images. We can prove this with a single magnifying lens that is held close to the eye. Objects further then 2/3 the focal length of the lens will be out of focus.

All optical systems are design around focus. In order to vary magnification and brightness, focus has to be constant. We may compromise magnification for brightness and visa- a- verse, but we can never compromise focus. Therefore, instead of saying that magnification M is inversely proportional to brightness, it is also accurate to say that magnification M is equal to focus divided by brightness B, where focus is a constant D.

M = D/B

Magnification power (M) = focus constant (D) / Brightness (B) Within know optical telescope design, all three factors are integrated. Focus has been the primary factor for rendering a clear image, while magnification and brightness both serves as a secondary factor in the appearance of a focused image. For known optical systems, focus, brightness, and magnification are inseparable. The resolving power is used to sum up the performance of a telescope. It is established by the telescope's ability to imprint details within an image. A picture is the imprint of individual dots that comes together to form a complete picture. Magnifying a picture involve stretching these dots. Light magnification is much different from picture magnification, and magnifies by changing the angle of the received image light.

But there is the breakthrough question, what if these three important factors could be isolated and individually tuned? Hm mm. Telescope engineering will not be the same again, and the science of astronomy will explode.

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