Numerical aperture formulawith refractive index

Students working in pairs or in small groups will predict how to best make a rainbow using the materials from the Science, Optics and You package. While they are working, darken the classroom as much as possible. The most brilliant spectrums are produced when the room is very dark.

Students will compare the rainbows that they produce with other groups of students and identify the colors that they see in their science notebooks. You may want to introduce the term color spectrum to help students describe what they see. Have students compare their earlier predictions with what they observe. Students should also draw diagrams in their science notebooks that show how a prism separates the colors of light.

Thus, this is all about what is a numerical aperture in optical fiber, the derivation of the numerical aperture of optical fiber, and its applications From the above information finally, we can conclude that the light-collecting ability is known as NA. So the value of NA should be high that can be attained simply once the dissimilarity between the two refractive indexes is high. For this, ƞ1 must be high otherwise ƞ2 must below. Here is a question for you, what is the value of NA?

Definition: The measurement of an optical fiber ability to collect the occurrence light ray in it is known as the numerical aperture. The short form of this is NA that illustrates the efficiency with the light which is collected within the fiber to get propagated. We know that when the light is propagated through an optical fiber during total internal reflection. So multiple total internal reflections take place within the fiber to transmit from one end to another.

The diagram of the optical fiber experiment is shown below. In the following image, a light ray that is transmitted into fiber optic is denoted with ‘XA’. Here ‘ƞ1’ is the refractive index of the core and ‘ƞ2’ is the cladding.

Narrative Writing - Use the following as a narrative writing prompt: We have all heard the myth that at the end of the rainbow you can find a pot of gold. Use your imagination and think of something else that you can find at the end of the rainbow. Now write a story about how you can reach the end of the rainbow and what you will find there.

In a very dark chamber, at a round hole, about one-third part of an inch broad, made in the shut of a window, I placed a glass prism, whereby the beam of the Sun's light, which came in that hole, might be refracted upwards toward the opposite wall of the chamber, and there form a colored image of the Sun.

Numerical apertureof lens

Reading - Share with students A Drop of Water by Walter Wick (ISBN 0590221973). The photographic essay investigates the three states in which water is commonly found and its properties in each state. An alternate choice could be Water by Ken Robbins (ISBN 0805022570), which is also a photographic essay. The beautiful hand-colored photographs combine black and white photography with an artist's interpretation of natural phenomena.

The numerical aperture is connected to the acceptance angle because the acceptance angle is the maximum angle during light travels through the fiber. Therefore the NA & acceptance angle is associated with each other.

Research - Isaac Newton and Rene Descartes discovered much of what we know today about rainbows. Using a variety of print and electronic media, students can research and write about the discoveries of Newton and Descartes. Older children can write stories about Newton and other scientists for younger ones and younger students can write for other classes.

We have already discussed that medium 1 is nothing but air, so the refractive index (ƞ) will be 1. So more especially we can say

As with the other activities, how much time you spend on this activity is up to you. However, it is recommended that you complete the activity in stages. The topic of rainbows can be the basis for an entire unit of study if you use this activity and the accompanying extensions as a launching point.

This incident ray travels within the fiber cable to get reflected totally through the interface of core-cladding. However, the incident angle must be more when contrasted to the critical angle or else, if the incident angle is low compare with the critical angle, then the ray gets refracted instead of reflected. Based on the law of Snell, the refracted ray & the incident angle will transmit within the same angle.

Music - Play recordings of songs about rainbows such as "Somewhere Over the Rainbow" or "The Rainbow Connection." Have students write their own verses for the songs or make up songs of their own.

Writing/Art - Have students draw and write a comic book version of the story of Newton's discovery. Each step of Newton's experiment should be depicted in the frames of the comic book. Students could then share the comic book with other students and other classes.

Optical fiber is a plastic or transparent fiber that is used to propagate light. The working principle of this is the total internal reflection from completely different walls. So light can be transmitted for long distances because the flexibility of fiber optics is sufficient. So this is used in microscopes which are in micro size, data communication, in fine endoscopes design, etc. An optical fiber cable includes three layers like core, cladding, and jacket. A core layer is enclosed through a cladding. Here cladding layer is normally designed with plastic or silica. The main function of the core within the optical fiber is to transmit an optical signal while the cladding directs the light in the core. As the optical signal is guided throughout the fiber, then it is called an optical waveguide. This article discusses an overview of the numerical aperture of optical fiber.

Newton believed that all the colors that appeared were in the sunlight shining into his room. If this was true, he thought, then he should be able to combine the colors and make the light white again. To test his idea, he placed another prism upside-down in front of the first prism. He was right. The band of colors combined again into white sunlight.

The following image illustrates the light ray is focused on an optical fiber. Here, the light ray travels from denser to rarer medium with an angle ‘α’ through the fiber axis. The ‘α’ angle is called the acceptance angle in the fiber optic cable.

Numerical apertureof optical fiber

Poetry - Have students write a poem about rainbows with lines for each color of the rainbow: red, orange, yellow, green, blue, indigo, and violet.

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Once the light ray is produced from the source of an optical fiber, then the optical fiber should be very efficient to get the maximum emitted radiation in it. So we can say that the efficiency of a light which is getting from the optical fiber is the main character once transmitting a signal throughout an optical fiber.

Reading/Writing - Choose poems (there are 70) from Rainbows are Made by Carl Sandburg (ISBN 015265481X) that relate to natural phenomena. Have students react to the poems and then write their own about rainbows, rain, or water.

On a sunny day, students can go outside and use sunlight through a prism to project a color spectrum on a piece of white paper. Or, cut a slit 1 cm wide and 15 cm long in a piece of black construction paper. Place the paper over the glass of an overhead projector so that just a slit of light is projected in a darkened room. Have students position a prism close to the projector, within the light beam, and experiment to find the most optimal placement for projecting a color spectrum. Another alternative is to have students spray a fine mist of water in bright sunlight to produce a rainbow, which is a particularly useful rainbow demonstration since, as with natural rainbows, water droplets are used. This can also be done in the classroom using an overhead projector projecting a slit of light. Spray a fine mist in front of the projector across the light beam. A color spectrum can be seen within the mist.

The numerical aperture of the optical fiber formula is derived above. So this is the formula for NA, where ‘ƞ1’is the refractive index for core & ‘ƞ2’ is the refractive index for the cladding.

Role Play - After reading aloud the vignette, have students research Newton's experiments and discoveries. Students can then write a skit depicting the day that Newton made his discovery about the properties of sunlight. Students will include imagined dialogue of Newton talking to his friends and family about his discovery.

Numerical aperture formulaexample

During the 1800s painters often joined government expeditions to the western wilderness of America. These painters rendered beautiful landscapes of the Rocky Mountains, Yellowstone, and Yosemite, which they displayed to the delight of the colonists in the eastern cities upon their return. In 1871 the painter Thomas Moran joined an expedition to Yellowstone in Wyoming, a location now well known for its waterfalls, hot springs, and geysers. Moran painted pictures of the beautiful scenes that he saw. These paintings were reproduced and became very popular. Moran's paintings helped make Americans aware of the natural wonders of the western wilderness. This awareness helped establish Yellowstone as the first national park in 1872. One of his paintings, Hot Springs of Yellowstone, shows a rainbow forming in the mist and steam rising from a naturally heated spring.

Water droplets in the air can act in a manner similar to that of a prism, separating the colors of sunlight to produce a spectrum known as a rainbow. To be able to see a rainbow, you must be standing with the sun behind you. The sunlight shines into the water droplets in the air, bending as it moves from the air into the water, reflecting off the sides the drops, and bending again as it exits the drops. As a result, all of the colors in the white light of the sun separate into the individual bands of color characteristic of a rainbow.

Numerical aperture formulain optical

In 1665 Isaac Newton was a young scientist interested in learning about light and colors studying at Cambridge University in England. One bright sunny day, Newton darkened his room and made a hole in his window shutter, allowing a beam of sunlight to enter the room. He then took a glass prism and placed it in the sunbeam. The result was a spectacular multicolored band of light that looked just like a rainbow.

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In fiber optics, it describes the angles range where light is occurring on the fiber optic will be broadcasted along with it.

Art/Current Issues - Ask students to select a natural or historical location in their neighborhood or city that is at risk or that they feel needs to be preserved. Students should then draw and color pictures of the site. They may choose to write letters to send to community leaders to encourage them to support its preservation. Students as a group can also paint a mural of the location.

The working principle of a fiber optic cable is total internal reflection where the light signals can be broadcasted from one position to another through a small loss of energy.

Discussion - After viewing Moran's Hot Springs of Yellowstone, or other landscapes from the same period, discuss with students how pictures can communicate intimacy for places they've never seen.

Newton needed to prove, however, that the colors came from the sunlight and not from the prism. To do this, he placed a card with a hole in it between two prisms, allowing only red light from the first prism to go through the second prism. The red light going through the second prism did not split into different colors, or turn white again; it remained red. Newton repeated the same experiment with all of the colors and got the same result. Thus, Newton proved that the colors came from the sunlight and were not, somehow, stored inside the prism.

Depending on the amount of light in the classroom and the intensity of the flashlights, students will have varying degrees of success in projecting color spectrums. The following are alternative methods to demonstrate the separation of white light into the color spectrum.

Expository Writing - Use the following as an expository writing prompt: We learned that raindrops can be like prisms and make a rainbow in the sky. Think about how sunlight moves through a raindrop and separates into the color spectrum. Now write a description of how rainbows are made.

Numerical apertureof microscope

There are various parameters that should be taken into reflection to select the suitable optical fiber in signal propagation.

The maximum angle completed through the light ray using the fiber axis to propagate the light via the fiber after the whole internal reflection is known as the acceptance angle.

Newton wrote about his discoveries in his book Opticks in 1704. His book has become one of the most important scientific books ever written. The following is a description of his experiment in his own words.

White light is composed of all the visible colors in the electromagnetic spectrum, a fact that can be easily proven through the use of a prism. As light passes through a prism, it is bent, or refracted, by the angles and plane faces of the prism and each wavelength of light is refracted by a slightly different amount. Violet has the highest frequency and is refracted the most. Red has the lowest frequency and is refracted the least. Because each color is refracted differently, each bends at a different angle, resulting in a fanning out and separation of white light into the colors of the spectrum.