Finally, if the beam is not collimated, i.e. it doesn't focus to a small spot on the core of the fiber, then the part of the beam that misses the core will not couple into the fiber.

Magnification ofmirror

Example 2: The distance of an object of height 6 cm from a concave lens is 20 cm. If its focal length is 10 cm, calculate the size and position of the image formed.

You can find questions on the power of lens and magnification on Vedantu.  It explains how it works and defines the lens formula and magnification. Practice questions about the lens formula provided on Vedantu to obtain a clear understanding of the concept. Vedantu also provides study resources for students in grades 1 through 12 as well as a number of competitive exams. The contents include notes, significant subjects and questions, revision notes, and other things. On Vedantu, you may access all of these resources for free. To have access to all of these resources, students must first register on the Vedantu website. You can also register through Vedantu's mobile app.

We use a cage system system with a 5 mm lens and a FC/APC (Angled Physical Contact) fiber plate to couple 633 nm laser light into an APC single mode fiber. Pretty much everything of the optical equipment is from Thorlabs.

When you are using APC facet of your receiving fiber, you should set a proper angle for that fiber due to misaligment between laser beam (it can be considered to be plane wave) and the fiber. Once you realign the APC fiber with a small angle (let's say 8 degree) then attach to the laser beam path, you will increase the coupling efficency.

For spherical lenses, the lens formula holds true in all scenarios. The third can be calculated if either of the first two is known.

Check whether your fibre entry is angled appropriately (the fibre end of the fibre connector you mentioned is angle-cleaved, the angle plate has to be mounted such that the angle of incidence with respect to the fibre end facet increases, rather than decreases), see image below (input beam should be along the beam path labelled 'output beam'): Image from https://www.thorlabs.com/images/TabImages/FC-APC_Coupling_dwg_780.gif.

Rainbow formation: After the rain, a rainbow appears. When a ray of light travels through raindrops, it is dispersed into its seven constituent colors, forming a rainbow in the sky.

Magnification of lensformula

With the setup you describe I would expect to get 60% without too much effort. Optimizing the mode matching to the fiber as described by @jayann should get you up to 80%. An experienced person could do all of this in a day, but if you are new to alignment of optics then it will take longer.

Magnification is defined as the ratio of image height to object height, or the ratio of image distance to object distance. The letter 'm' is commonly used to represent it.

Magnification ofconvexlensis positive or negative

More than likely it is a mode matching issue. Start by looking up the mode coming out of the laser (or measuring it with a beamscan) and the mode accepted by the fiber. You need to use ABCD matrices to choose the proper lenses to put in between. If you don't want to put all of this effort in, then use the solution discussed by @jayann where you add a 1 to 1 telescope (equal focal lengths placed 2 focal lengths apart) in the beam upstream of the fiber coupler. Mount one of the lenses on a movable stage and use this to optimize the mode matching to the fiber.

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How much light couples into the fiber depends on the NA (numerical aperture) of the fiber, the diameter of the beam of light entering the collimating lens, and the focal length of the lens. Typical fibers accept light only from a limited angle about the axis of the fiber. This is referred to as the NA of the fiber. If the NA is large (e.g. 0.7) the fiber can accept light at up to about 44 degrees from the axis. For an optical fiber this would be a remarkable NA. Most fibers are in the 0.2 range and can accept light only within about 10-12 degrees from the axis.

Magnificationformula Biology

The degree of divergence or convergence of a beam of light caused by a lens is measured in the power of the lens. The focal length of a lens determines the degree of convergence and divergence. The letter 'P' stands for the lens's power. A lens's power is proportional to its focal length.

Because you will never be able to align your coupling setup absolutely perfectly, optimising the coupling efficiency is not an optimisation with a single maximum. A good strategy is usually to maximise the coupling for a given z-position (along axis through fibre length-wise) using the x-y-position adjustments of your fibre dock (plane perpendicular to fibre axis). Note the maximum achieved throughput and move the z-position a little bit. Repeat. If the achieved maximum is smaller, move z the other direction. If it's larger, you're moving in the right direction.

Magnificationformulaofmirror

This one is time-consuming but if the project is very efficiency-hungry, then it's worth a try. Assuming you have chosen the correct lens and incoming spot-size of the beam (matched to the NA of the fiber i.e.) but a high efficiency still eludes you, then:

A good tip mentioned already in one of the comments above is to connect a fibre-coupled source to the other end of the fibre, and do the inital alignment 'backwards', collimating the output beam. This will result in a focussing lens position that is already pretty close to where it needs to be.

Coupling into a fibre is something that becomes a lot easier with experience/practice. The first couple of times it can be hugely time consuming. Here's a couple of things I would check/do:

The power of a lens is its ability to converge the light rays falling on it. In other words, it is the measure of the degree of convergence or divergence of the rays of light falling on the lens. As the degree of convergence or divergence of the rays depends upon the focal length of the lens, the power of the lens can be defined as the reciprocal of the focal length of the lens. For instance, if the focal length (f) of a lens is 1 m, the power of the lens (p) is equal to 1/f = 1/1 = 1 dioptre. The SI unit of power of a lens is dioptre and often denoted by D. Note that as the focal length of a concave lens is negative, the power of this type of lens is negative (-), whereas the power of a convex lens is positive (+) as the focal length of this lens is positive.

*With "should" and "reasonable time" I refer to coupling efficiencies one can achieve at time scales on the order of tens of minutes rather than hours, days, weeks.

Lenses, both converging and diverging, are the marvels of optical physics that use the ability of these media to refract, reflect, or bend light rays. In general, the lenses come in two shapes: convex (curved outward) and concave (curved inward). One of their principal purposes is to magnify images, i.e., make images appear larger than their actual size. Nowadays, these lenses can be seen in microscopes, telescopes, binoculars, other optical instruments, and of course, in our own eyes. Scientists and students have many simple to complex algebraic equations to associate the shape and physical dimensions of a lens to the effects it puts on the light rays that pass through it. Here, we will learn and understand some of the most vital equations and formulae related to the lens, along with the lens power. We will also learn how to calculate magnification with the help of lens formula.

Magnification ofconvexlens

Example 1: If the distance of the object placed in front of a convex lens having a focal length of 10 cm is 15cm, find magnification. Also, tell the characteristics of the formed image.

A convex lens with a short focal length converges the light rays closer to the focal point, while a concave lens with a short focal length diverges the light rays closer to the focal point.

Position of the fish in the pond's water: The ray from the pond's fish bends away from the incident's normal path. The emergent ray, which appears to be a fish, is seen just above its position.

Magnification of lenscalculator

Where v is the image distance, u is the object distance, and f is the lens focal length. The optical center of the lens is used to estimate the distance between the object and the image. The distance symbol is used according to the convention.

From the results, we can conclude that the image is virtual, has a height of 2 cm, is on the same side as the object, and is at a distance of 6.7 cm from the concave lens.

Magnification of lensin physics

From these results, we can say that the image is real, inverted, magnified 2 times, on the opposite side of the object, and at a distance of 30 cm from the lens.

If you are only getting 30%, then either your fiber is bad or your mode matching solution is wrong. You can check to see if the fiber is bad by looking at the transmitted light on a CCD. If the beam doesn't look like a nice Gaussian beam, then your fiber is not single mode and you have a problem.

Make sure you align your beam nice and parallel to the fibre axis. This is particulary important if the acceptance angle of your fibre is quite small. This is best done with an iris that is set to a height in the middle of the range of your 3-axis stage, and if you're using a top plate with a groove where your fibre mount slides into, you can use an iris that uses the same groove to align your beam along the z-axis.

Sun visibility slightly before sunrise: When the sun's rays enter the atmosphere (which is a denser material than vacuum), they bend away from normal to the incidence due to refraction. Because humans perceive the sun's refracted beams, the sun becomes visible shortly before sunrise.

When the focal length is expressed in meters, the power of a lens is expressed in dioptres. As a result, a lens with a focal length of one meter has a power of one dioptre.

After having finished fiber coupling, i.e. positioning the tip of the fiber as precisely as possible in the beam path, beam walking (usually performed with two mirrors that lead the beam to the fiber-coupling stage) can also help in elevating the efficiency and can be performed in a matter of minutes.

A positive (+) sign of magnification indicates that the image is virtual and erect, whereas a negative (-) sign indicates that the image is real and inverted.

Images formed by these lenses can be real, virtual, or of different sizes depending on the objects’ distance from the lens. Now, the Lens formula helps us in calculating the image distance. It is the formula, or we can say the equation that relates the focal length, the distance of the object, and the distance of the image for a lens. It is given as:

The lens formula is applicable to both types of lenses - convex and concave. It can also be used to calculate image distance for both real and virtual images. If the equation provides a negative image distance, then the image formed is virtual and on the same side as the object. However, if the equation provides a negative focal length, then the lens is diverging, not converging.

I am in AMO Physics and work a lot with optics. I just wanted to get an idea of what coupling efficiencies one "should" get in a "reasonable time"* by coupling light into a fiber using different couplers, like collimators, mounting plates, mounted lens systems, etc. I understand that this dependents on a lot of factors, so I will narrow it down for my specific case but would appreciate if ppl report some numbers with a short info about their setups.

Spherical lenses in optical physics are the lenses formed by coupling two spherical surfaces together. Based on this concept of formation by binding two surfaces, these lenses are of two types: convex lenses - the lenses formed by binding the two spherical surfaces curved outward and concave lenses - the lenses formed by binding the two spherical surfaces curved inward.

Assuming that you have collimated light to start with, the diameter of the beam and the focal length of the lens then determine the effective NA of the light converging on the fiber. The NA is the ratio of the radius of the beam to the focal length of the lens (this is a little approximate since NA is defined as the sin of the half angle, but for normal NA's it is very close). If the converging beam of light has too great an angle, the outer parts of the beam will fail to couple into the core of the fiber.

I realise this is an old question, but this is something that most newcomers to fibre optics struggle with, so I thought some more practical tips might be useful to others stumbling across this question.

Students should study the theory on the Power of lens given on Vedantu or in their textbook first. Make an effort to understand the formulas and notations. Solve as many problems as you can once you have understood the concept. Solving problems will help you better understand how lenses function, what a lens' power is, and what magnification means. The problems, as well as notes, are available for free on Vedantu. Solving problems will help you identify your weak areas. Learn more about those topics and answer more questions.

When a pencil is placed in a glass of water, it bends: When a pencil or stick is placed in a beaker or a glass of water, it seems slightly twisted. This occurs when light traveling from the rarer medium of air to the denser medium of water bends towards the incident, giving the impression of a bent pencil or stick.

The reason for my question: My PI told me I should get efficiencies up 80% percent with our coupling scheme but I can only get 30%. I hope to get a better feeling for coupling efficiencies with this answer.

Magnification is defined as the ratio of the height of the image formed to the height of the object. In terms of distance of image and object, it is defined as the ratio of image distance to the object distance. For instance,

Check your fibre end facet with a fibrescope or under a microscope. If it's damaged or dirty you will never achieve good coupling efficiency.