# Focal length measurement and definition in DSLR cameras [duplicate]

So i am a bit confused when it comes to focal length in DSLR cameras. According to multiple sources online i found and as per NIKON "It is a calculation of an optical distance from the point where light rays converge to form a sharp image of an object to the digital sensor or 35mm film at the focal plane in the camera".

However according to other explanations it is the distance from the lens to the point where light converges

Therefore my first question is this. If the focal length is the distance from the convergence point to your camera sensor and since the image is the sharpest where the refracted beams of light meet how is the image not blurry since the location of the "intersection" is different from the location of the sensor.

Therefore to put it plainly, since through the pentaprism we are viewing a perfectly clear/focused image is the converging point at the prism, the sensor or somewhere else. Lets keep it simple by talking about a 50 mm lens.

Secondly how is technically and inside the camera the refraction amount by the lens translated to a wide angle or telephoto lens.

I apologise for the confusion.

Thank you

• I think this would be better separated into one or more more focused questions, because it's hard to address everything you are wondering on one slid answer. May 11, 2018 at 16:15
• @mattdm +1 for " focused questions " that punny. May 12, 2018 at 20:55

The viewscreen upon which the viewfinder image is projected is (hopefully) the exact same optical distance from the lens as the sensor is. The mirror that reflects the light up onto the viewscreen has some very precise adjustments that allows the needed precision. WHen the mirror flips up to take the picture, the distance the light travels in a straight line is the same as the distance it travels when reflected by the mirror to the focusing screen.

• .Hi thanks for your answer. ! Above makes sense for a single light ray coming through the center of the lens and traveling parallel to the lens .Now im not an optics expert however from what i understand in reality you have multiple light rays coming from different angles and then converging on a single point. So i understand per your above how that would work with a single ray through the middle but not for an actual case unless light is refracted eventually to a parallel line relative to the camera axis. May 11, 2018 at 14:30
• The path through the centre of the lens to strike the centre of the sensor is the one for which Michael is most obviously right, but closer consideration will show you that he's right for any possible light Ray passing through that system. Imagine any light path you like, if it helps you could even print out the diagram and draw them in. Remembering that light bounces off a mirror so that it makes the same angle with the surface as it leaves as it did when it arrived, you can trace how any Ray would pass through and measure the paths with and without the mirror. May 11, 2018 at 21:22
• What we (and the camera) sees is light reflecting in all (ok nearly all) directions. Our camera lens captures some of them (bigger front element captures more). When in focus, all the light the lens captures from a point B will be focused to a point B'. See this simple diagram: scientificsentence.net/Optics/image_converging.png that shows three rays traced through the lens. Any ray that reflects off of B and hits the lens will end up meeting again a B'. Not just the ones that go through the centre. Some simplification but that is the concept. May 11, 2018 at 21:33
• @IasonManolakis Examine the diagram carefully. Notice that the part of the mirror that is closer to the focusing screen is also closer to the sensor than the parts of the mirror that are further from both the focusing screen and the sensor. This is because the mirror bisects the angle between the sensor and focusing screen. Any spot on the front surface of the mirror, which is the one that is coated, is the same distance from both the sensor and the focusing screen. May 12, 2018 at 6:22

The job of the camera lens is to project an image of the outside world onto the surface of film or digital sensor. This is accomplished by altering the direction of incoming light rays. This action is called refection (Latin bend inward). In other words, light from the subject enters the lens. Refection occurs and the light rays bend inward, the revised path of the light traces out the shape of a cone. The focal length is a measurement made from the center of the lens to the apex of this cone when the lens is imaging a far distant object. If the lens is imaging a nearby object, the distance lens to cone apex is elongated. This elongated distance is now called the “back focus”. Again, the focal length is that measurement taken when the lens is imaging an object at infinity (as far as the eye can see).

The fact that focal length is a measurement from the center of the lens to the apex of the cone of image forming rays is true only for a simple lens. Camera lenses are not simple. They are complex arrays of lenses. Some will have positive power, some negative power. Some will be cemented together; some will be air-spaced. Such a complex array is necessary to mitigate lens defects called aberrations.

The fact that camera lens is complex shifts the optical center. In other words, the point associated with the lens that we measure from is not likely the center of the lens barrel. Actually there are two cardinal measuring points. Front nodal point is used to measure subject distance from the lens. Rear nodal point is used to measure focal length. These are difficult to locate; we use an optical bench setup.

A key point, we measure from the rear nodal to apex of cone of light to find the focal length, and this is performed when the lens is imaging an object located at infinity. If the object is closer than infinity, the back focus distance is longer than the focal length. This fact is why we must move the lens away from film or sensor to obtain focus when imaging an object not at infinity. This act is called focusing.

When we focus, a sharp image will be obtained if the apex of this cone of image forming rays just kisses the surface of the film or digital image sensor. Such a kiss images the cone as a tiny circle of illumination. If the distance lens to sensor (or film) is wrong, this circle will be larger. Sharpness is obtain only when this circle is so small that it will be perceived as a point of light, a point has no desirable dimension. As an example, newspaper photos appear un-sharp because the dots of ink that comprise the image are too big, they are desirable.

“Therefore my first question is this. If the focal length is the distance from the convergence point to your camera sensor and since the image is the sharpest where the refracted beams of light meet how is the image not blurry since the location of the "intersection" is different from the location of the sensor.”

Answer: We focus by moving the lens forward and backward. This act adjusts the position of the apex (intersection) so that it just kisses the surface of the sensor. This act results in a tiny circle of illumination being recorded. This circle is called the “circle of confusion” because under the microscope it is seen with scalloped edges and it is juxtaposed with all the other circles of confusion that make up the image. To appear as sharp, this circle, the smallest fraction of an image, must be 0.5mm in diameter or less when viewed from standard reading distance.

In the SLR design, the image forming rays are diverted for viewing and composing via a mirror and pentaprism. The falls on a roughed up glass screen (ground glass viewing screen). The distance rear nodal to sensor and rear nodal to viewing screen are carefully maintained so they are identical.

“Secondly how is technically and inside the camera the refraction amount by the lens translated to a wide angle or telephoto lens.”

Answer: When we fit lenses with a focal length that is approximately equal to the corner to corner measurement of the sensor, the angle of view will be classified as “normal”. This will be about 45° when the camera is held horizontal (landscape). If the focal length is shorter, say 70% of this value, or shorter, the angle of view is classified as wide-angle. If the focal length is 2X this value, or longer, the lens will be classified as telephoto.

So far, we are describing how light rays from an object on optical center preform. The film/sensor is being bombarded by billions and billions of rays from everything within its field of view. Points emanating from all these objects, each trace out an image cone of light. Each will have a different length depending on subject distance. We stop down the lens using a restriction called an aperture. This reduces the working diameter of the lens.

Such a restriction reduces the diameter of the base of image cone. This act of stopping down , yields a skinny image forming cone of light. Imagine two sharpened pencils pointy end to pointy end. The narrower the pencils, the more tolerance fore and aft of the apex and we still get a tiny circle. All we need is 0.5mm.

The rub is, today’s miniature cameras yield an image too tiny to be useful. We must enlarge them perhaps 8X or even 12X to get an 8X10 inch image. Thus the circle size at the sensor must be super tiny to support this blowup. Industry stand for good focus is a circle 1/1000 of the focal length. Thus for a 50mm lens the circle size at the image plane is 50mm ÷ 1000 = 0.05mm. For precision work we often use 1/1500 of focal length, that’s 0.033mm. Did you ever dream of such exactness?