This shows parallel beams from two helium-neon lasers converging to the principal focal point of a 30 cm double convex lens. The rays then enter a diverging lens of focal length -10cm on the right. The laser beams were made visible with a spray can of artificial smoke.

Focal lengthof lens formula

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Camerafocal lengthcomparison

Most magnifying glasses are double-convex lenses and are used to make objects appear larger. This is accomplished by placing the lens close to the object to be viewed. In this way the light rays are bent toward the center of the lens. When these bent rays reach the eye they make the object appear much larger than it actually is. However, if the object is far enough away from the lens, the image will flip, appearing smaller and upside down. The distance at which this flip occurs is twice the focal length (the distance from the optical center of a lens to the point where the light rays converge) of the lens. The focal length of any lens is determined by the amount of curve on the lens’ face. The magnified image is called a virtual image while the smaller, inverted image is called the real image.

The magnifying glass was the forerunner of the compound microscope (in which a series of lenses are used to focus, magnify, and refocus an image), one of the basic tools used in medicine.

Focal lengthexamples

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Lenses and focal lengthchart

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Lenses and focal lengthcomparison

The most important characteristic of a lens is its principal focal length, or its inverse which is called the lens strength or lens "power". Optometrists usually prescribe corrective lenses in terms of the lens power in diopters. The lens power is the inverse of the focal length in meters: the physical unit for lens power is 1/meter which is called diopter.

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Camera lens distance chart

Canonlenses and focal length

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The principal focal length of a lens is determined by the index of refraction of the glass, the radii of curvature of the surfaces, and the medium in which the lens resides. It can be calculated from the lens-maker's formula for thin lenses.

Many people have used a magnifying glass and sunlight to ignite a piece of paper. When the lens is held at exactly two focal lengths from the paper, all of the light will be concentrated into a tiny point, generating enough heat to start a fire.

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For a thin double convex lens, refraction acts to focus all parallel rays to a point referred to as the principal focal point. The distance from the lens to that point is the principal focal length f of the lens. For a double concave lens where the rays are diverged, the principal focal length is the distance at which the back-projected rays would come together and it is given a negative sign. The lens strength in diopters is defined as the inverse of the focal length in meters. For a thick lens made from spherical surfaces, the focal distance will differ for different rays, and this change is called spherical aberration. The focal length for different wavelengths will also differ slightly, and this is called chromatic aberration.

The magnifying glass is one of the most ancient optical devices known to science. Thousands of years ago Egyptians used chips of crystal or obsidian (a type of shiny stone) to better view small objects. In Rome Emperor Nero (a.d. 37-68) was known to have peered through gemstones at actors on a distant stage. The first magnifier constructed for scientific purposes is believed to have been designed by the English philosopher Roger Bacon (circa 1220-1292) sometime during the thirteenth century.