Category: Focal length formula

Focal length formula

Before the s, simple lenses dating back as far as the Romans and Vikings allowed limited magnification and simple eyeglasses. Zacharias Jansen and his father combined lenses from simple magnifying glasses to build microscopes and, from there, microscopes and telescopes changed the world. Understanding the focal length of lenses was crucial to combining their powers. There are two basic types of lenses: convex and concave. Convex lenses are thicker in the middle than on the edges and cause light rays to converge to a point.

Concave lenses are thicker on the edges than in the middle and cause light rays to diverge. Convex and concave lenses come in different configurations. Plano-convex lenses are flat on one side and convex on the other while bi-convex also called double-convex lenses are convex on both sides.

Lens Formula

Plano-concave lenses are flat on one side and concave on the other side while bi-concave or double-concave lenses are concave on both sides.

A combined concave and convex lens called concavo-convex lenses is more commonly called the positive converging meniscus lens. This lens is convex on one side with a concave surface on the other side, and the radius on the concave side is greater than the radius of the convex side.

A combined convex and concave lens called a convexo-concave lens is more commonly called a negative divergent meniscus lens.

This lens, like the concavo-convex lens, has a concave side and a convex side, but the radius on the concave surface is less than the radius on the convex side. The focal length of a lens f is the distance from a lens to the focal point F. Light rays of a single frequency traveling parallel to the optical axis of a convex or a concavo-convex lens will meet at the focal point. A convex lens converges parallel rays to a focal point with a positive focal length. Because the light goes through the lens, positive image distances and real images are on the opposite side of the lens from the object.

The image will be inverted up-side down relative to the actual image. A concave lens diverges parallel rays away from a focal point, has a negative focal length and forms only virtual, smaller images. Negative image distances form virtual images on the same side of the lens as the object.

The image will be oriented the same direction right-side up as the original image, just smaller. Finding focal length uses the focal length formula and requires knowing the distance from the original object to the lens u and the distance from the lens to the image v. The lens formula says that the inverse of the distance from the object plus the distance to the image equals the inverse of the focal distance f.

The equation, mathematically, is written:. To find the focal length of a lens, measure the distances and plug the numbers into the focal length formula. Be sure all measurements use the same measurement system. Example 1 : The measured distance from a lens to the object is 20 centimeters and from the lens to the image is 5 centimeters.

Completing the focal length formula yields:. Example 2 : The measured distance from a lens to the object is 10 centimeters and the distance from the lens to the image is 5 centimeters. The focal length equation shows:.The focal length of an optical system is a measure of how strongly the system converges or diverges light ; it is the inverse of the system's optical power.

A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly.

For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated parallel rays are brought to a focusor alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam.

For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power. In most photography and all telescopywhere the subject is essentially infinitely far away, longer focal length lower optical power leads to higher magnification and a narrower angle of view ; conversely, shorter focal length or higher optical power is associated with lower magnification and a wider angle of view.

On the other hand, in applications such as microscopy in which magnification is achieved by bringing the object close to the lens, a shorter focal length higher optical power leads to higher magnification because the subject can be brought closer to the center of projection.

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci or focal points of the lens. For a converging lens for example a convex lensthe focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens for example a concave lensthe focal length is negative, and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.

When a lens is used to form an image of some object, the distance from the object to the lens uthe distance from the lens to the image vand the focal length f are related by. The focal length of a thin convex lens can be easily measured by using it to form an image of a distant light source on a screen.

How to Calculate Focal Length of a Lens

The lens is moved until a sharp image is formed on the screen. Determining the focal length of a concave lens is somewhat more difficult. The focal length of such a lens is considered that point at which the spreading beams of light would meet before the lens if the lens were not there. For a thick lens one which has a non-negligible thicknessor an imaging system consisting of several lenses or mirrors e.

If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium n is the refractive index of the substance from which the lens itself is made; n 1 is the refractive index of any medium in front of the lens; n 2 is that of any medium in back of it.

In general, the focal length or EFL is the value that describes the ability of the optical system to focus light, and is the value used to calculate the magnification of the system. The other parameters are used in determining where an image will be formed for a given object position.

The corresponding front focal distance is: [3]. In the sign convention used here, the value of R 1 will be positive if the first lens surface is convex, and negative if it is concave. The value of R 2 is negative if the second surface is convex, and positive if concave. Note that sign conventions vary between different authors, which results in different forms of these equations depending on the convention used.Joinsubscribers and get a daily digest of news, geek trivia, and our feature articles.

By submitting your email, you agree to the Terms of Use and Privacy Policy. In photography, we use focal length as a primary descriptor of lenses. The purpose of a photographic lens is to take parallel rays of light and converge them into a single point of focus so they can be recorded, either on a piece of film or, far more commonly, with a digital sensor.

The point where the lens causes the light rays to converge is called the focal point. In the image at the top of the article, the parallel rays of light entering the lens are represented by the two red arrows.

Without a lens to focus the light for your camera, all you get is a blurry mess. The focal length of a convex lens is the distance between the center of the lens and the focal point. Unfortunately, the lenses we use for photography are a lot more complex than a single convex lens. They generally have multiple different lens elements that work together to converge light with as few optical aberrations as possible. Instead, focal length is measured from the rear nodal point—which, along with the focal point, is one of the cardinal points in Gaussian optics —to the focal point while the lens is focused at infinity.

The reason we use focal length to describe lenses is because it tells us one very important thing: what the field of view of that lens will be. And since the sensor remains the same size regardless of what lens you use, the field of view tells us how much a lens can magnify distant subjects.

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Photographic lenses generally have a focal length of between 14mm and mm, although there some expensive exceptions that have shorter or longer focal lengths. The shorter the focal length, the wider the field of view. The longer the focal length, the narrower the field of view. The human eye has a focal length of somewhere between 40mm and 58mm, with 50mm being the usual compromise. Any lens with a focal length shorter than that normal focal length is a wide angle lens and things in the image will appear smaller than they look to your eyes.

Focal length

Any lens with a focal length longer than the normal focal length is a telephoto lens and things in the image will appear larger. Normal lenses are great for casual photography and portraits. Focal length is the most important measurement of a photographic lens. It, along with the apertureare what tell us how a lens will affect our images.

Image Credits: Henrik via Wikipedia. The Best Tech Newsletter Anywhere. Joinsubscribers and get a daily digest of news, comics, trivia, reviews, and more. Windows Mac iPhone Android. Smarthome Office Security Linux. The Best Tech Newsletter Anywhere Joinsubscribers and get a daily digest of news, geek trivia, and our feature articles.

Skip to content. How-To Geek is where you turn when you want experts to explain technology. Since we launched inour articles have been read more than 1 billion times. Want to know more?Last updated at April 26, by Teachoo. Note : - We follow the sign convention for lenses In the image, the red text is negative, and blue text is positive.

Example At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced by the lens. View Answer. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image. Also find its magnification. Will this lens produce a complete image of the object?

Verify your answer experimentally. Explain your observations. Draw the ray diagram and find the position, size and the nature of the image formed.

How far is the object placed from the lens? Draw the ray diagram. On signing up you are confirming that you have read and agree to Terms of Service.

Facebook Whatsapp. About the Author Davneet Singh. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo. Teachoo is free. Login to view more pages. Or login Sign In.For instance, mm means that the lens can be anywhere from 15 mm 30 mm. Of course, that explains it, right?

This element determines the actual or equivalent angle of view and hence visible area of the lens on the given camera. A lot of photographers with the two most common sensor crop factors: 1.

So, the clue is the diagonal dimension of the sensor. The crop factor is the ratio on the full-frame diagonal to the diagonal of the sensor we calculate.

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Pythagorean theory will help us to calculate the diagonal knowing both horizontal and vertical sides of the rectangle. The dimensions of the full-frame sensor are 24mm and 36mm. To find a crop factor of any given sensor, we need to calculate the diagonal. The standard focal length is what the manufacturer writes on the lens.

But the crop factor affects it.

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So, the effective focal length is the actual resulting value that the lens has on the camera with the crop factor adjustments. For your reference, sometimes it is called Effective Focal Range. As you can see with the same physical focal length F, the angle a2 is smaller than a1. This fact means that on the cropped sensor you actually see the narrower area through the viewfinder. In reality, this narrow fielf of view effect is the same effect as if you zoomed in a little bit.

And so this virtual zoom in focal length is the effective focal length. Hopefully, it clarified things instead of making them even fuzzier. And finally, we made it to the magic formula that will help you to understand what your lens is capable of. As simple as that. This focal range increase naturally affects the angle of view because the longer the focal length, the narrower the angle. In other words, the 24mm lens with the 24mm set as current focal length delivers 36mm on the camera with 1.

For a landscape it can be bad, rendering your wide lens not as wide. As opposed to the telescopic lens, where it increases your reach. The table below shows some common crop factors for the modern cameras.

With those values, you can easily calculate the effective focal length and know your photographic equipment better.

focal length formula

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focal length formula

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focal length formula

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