Normal or standard lenses have a focal length between 35mm and 50mm in full-frame terms. When comparing across formats, they have a field of view that’s also equivalent to a normal lens. These lenses best duplicate how we see the world.

Understanding focal length in photography can feel a bit overwhelming when trying to account for all of the ways it changes the properties of an image. Below, I’ve outlined the focal length differences across the major fields of view.

Photographs taken with short focal lengths show distortion in certain elements; those closer to the foreground are magnified whereas all the elements in the background will show a diminished perspective.

Spot sizeformula

After multiplying both sides by the denominator from the left side of the equation and then multiplying both sides by (w0')2, Equation 14 becomes:

Super telephoto lenses have very different focal lengths, ranging from 300mm and beyond. When considering focal length and field of view, crop factor is incredibly important because you can gain significant amounts of reach using a crop sensor like Micro 4/3rds.

This concept can be complicated when the crop factor and the field of view come into play since we began to ask what is the equivalence of the focal length of a lens using it in a camera with a different sensor format.

It’s important to consider that focal length is a static property of a lens that’s true regardless of crop factor; for example, a 16mm APS-C lens is a 16mm lens even if it has a 24mm equivalent field of view in a full-frame camera. We’ll see + in-depth info about this below.

Many laser optics systems require manipulation of a laser beam as opposed to simply using the “raw” beam. This may be done using optical components such as lenses, mirrors, prisms, etc. Below is a guide to some of the most common manipulations of Gaussian beams.

Both of these results intuitively make sense because the beam’s wavefront is approximately planar both at and very far away from the beam waist. At these locations, the beam is almost perfectly collimated (Figure 9). According to the standard thin lens equation, a collimated input would have an image distance equal to the focal length of the lens.

Please note that lens compression is not related to the lens, but to the distance from the subject (Ex. You can achieve the same field of view and perspective shooting an element with a short focal length like 20 mm or cropping the same area from a 50 mm as long as both images are taken from the same distance).

When you look at the focal length of the lens in question and you see a number below 35mm, you know you’re looking at a short focal length.

In Equation 1, I0 is the peak irradiance at the center of the beam, r is the radial distance away from the axis, w(z) is the radius of the laser beam where the irradiance is 1/e2 (13.5%) of I0, z is the distance propagated from the plane where the wavefront is flat, and P is the total power of the beam.

For example, if I use a short focal length in portrait photography, parts of the body that are closer to me can be unflatteringly emphasized. On the other hand, in genres like landscape photography, it’s more common to see images taken with a wide-angle view, not only to capture the entire scene in a single image but to emphasize elements in the foreground.

In addition to describing imaging applications, the thin lens equation is applicable to the focusing of a Gaussian beam by treating the waist of the input beam as the object and the waist of the output beam as the image. Gaussian beams remain Gaussian after passing through an ideal lens with no aberrations. In 1983, Sidney Self developed a version of the thin lens equation that took Gaussian propagation into account4:

Laser beam spot sizechart

Telephoto lenses are those beyond 50mm. These lenses are also physically longer than wide and normal lenses. The field of view is smaller but you gain significant reach.

Laser spot sizedefinition

A prime lens can’t be adjusted and its focal length and field of view are fixed. The trade-off for flexibility in focal length is usually a wider aperture and better image quality because the prime lens can be optimized for its angle of view. Usually but not always; some top-quality zoom lenses nowadays are absolutely comparable to prime lenses in terms of quality for a given focal length.

In order to understand the beam waist and Rayleigh range after the beam travels through the lens, it is necessary to know the magnification of the system (α), given by:

Focal length is the physical measurement of distance between the lens and the imaging sensor when the subject is in focus.

So what are the mm in lenses? The key is to understand that focal length is calculated by measuring the distance from the optical center of the lens to the image sensor, and this distance is measured in mm. The longer the focal length, the physically longer the lens will be. Lenses with a wider view will have a shorter focal length and are physically shorter by comparison.

Lens focal length is a surprisingly nuanced topic! A simple physical measurement leads to so many considerations that go into how an image is composed. From the angle of view to depth of field, no aspect of a photograph goes untouched.

Diodelaser spot size

As we step into normal focal lengths, which are closer to our human vision (like 35mm), this effect is subtle to invisible. However, once we hit telephoto angles of view, the background appears to be closer to the subject. This effect increases as your lens mm does.

Photos taken with a long focal length look more “compressed” as compared to shorter focal lengths, and allow you to capture subjects from a farther distance without losing image quality.

The other limiting situation where the lens is far outside of the Rayleigh range and s >> zR, simplifying Equation 18 to:

Similarly to when s << zR, the calculations for the output beam waist, divergence, Rayleigh range, and beam waist location are also simplified:

A lens focal length that’s greater than 50mm is considered a long focal length. This view is narrower than the normal view we’re accustomed to when paying bare attention. An image taken with a 100mm telephoto lens will have a much smaller section of coverage than a normal or wide-angle field of view.

Focal length in photography comes up far more often than focal distance, which is an entirely different property of a lens. Focal distance is related to focal length but is not dependent on it.

Achieving a truly collimated beam where the divergence is 0 is not possible, but achieving an approximately collimated beam by either minimizing the divergence or maximizing the distance between the point of observation and the nearest beam waist is possible. Since the output divergence is inversely proportional to the magnification constant α, the output divergence reaches a minimum value when |s| = f (Figure 11).

Focal length comparisons are incomplete without the infamous crop factor discussion. Nowadays, we have APS-C, Micro 4/3rds, medium format, and full-frame, all of which use a lens focal length description centered around 35mm film gear. While this made sense when the digital revolution began, it’s often simply confusing to parse nowadays.

In the relation between focal length and depth of field, when all other values are equal, short focal lengths (or wide angles of view) have deeper depth of field relative to long focal lengths (narrow fields of view). Thus, the longer the focal length, the farther the hyperfocal distance will be.

There are two limiting cases which further simplify the calculations of the output beam waist size and location: when s is much less than zR or much greater than zR.3 When the lens is well within the laser’s Rayleigh range, then s << zR and (|s| − f)2 < zR2. Equation 18 simplifies to:

Camera zoom lenses allows to change the angle of view without moving and are more versatile than prime lenses. The downside is that maximum apertures are not usually as fast as the fastest prime lenses. For example, an f/1.4 zoom would be ridiculously expensive and massive.

The above equation will break down if the lens is at the beam waist (s=0). The inverse of the squared magnification constant can be used to relate the beam waist sizes and locations3:

Where w0 is beam waist before the lens and w0’ is the beam waist after the lens. The thin lens equation for Gaussian beams can then be rewritten to include the Rayleigh range of the beam after the lens (zR'):

As you can see, the focal length we choose affects the final image. Also, the field of view and lens distortions fundamentally affect the type of photography you do.

Wide-angle lenses or short focal lengths offer a great opportunity for shooting landscapes, cityscapes, Milky Way photography, and Northern Lights photography.

Hi Anne, it totally depends on the sensor size of the camera. For example, if you’re using a Micro 4/3 sensor camera with the 60mm f2.8 lens, since the crop factor is 2x, it means that you’re cropping the image the double, so technically it’s like shooting at 120mm focal length. Hope it’s clear. 🙂

Focal length can feel a little abstract when looking at one lens versus another. One of the easiest ways to understand focal length is to look at images that use the lenses in question! To wrap up, here are some focal length examples for you to consider:

Remember that if you tend to specialize in any type of photography, it’s crucial to understand how focal length affects your image so you can have a better idea of what sort of lenses you should be shopping with, as well as the impact they have on a subject and background. You can download my PDF photography guide to get more information about this.

The lengthy derivation is not covered in this text, but the beam radius at the target can be described by the following expression4:

In many applications, such as laser materials processing or surgery, it is highly important to focus a laser beam down to the smallest spot possible to maximize intensity and minimize the heated area. In cases such as these, the goal is to minimize w0' (Figure 7). A modified version of Equation 13 may be used to identify how to minimize the output beam waist3:

These lenses take on an expansive field of view that’s wider than what we normally pay attention to. An image taken with a 15mm lens will seem abnormally expansive, taking, for example, an entire landscape with ease.

Focalspot sizeformula

In Equation 7, s’ is the distance from the lens to the image, s is the distance from the lens to the object, and f is the focal length of the lens. If the object and image are at opposite sides of the lens, s is a negative value and s’ is a positive value. This equation ignores the thickness of a real lens and is therefore only a simple approximation of real behavior (Figure 4). The thin lens equation can also be written in a dimensionless form by multiplying both sides of the equation by f:

How focal length works is by describing each lens in terms of millimeters (lens mm). This description is a hard-physical reality of the lens in question, no matter the brand, format, or aperture.

Focal length touches upon many elements of the photography basics; composition, aperture, depth of field, and other aspects all shift when taking focal length into account! Each twist of the zoom ring or swap of a prime lens is a shift in the interplay of focal length and your creative vision.

The Rayleigh range of a Gaussian beam is defined as the value of z where the cross-sectional area of the beam is doubled. This occurs when w(z) has increased to √2 w0. Using Equation 4, the Rayleigh range (zR) can be expressed as:

However, this irradiance profile does not stay constant as the beam propagates through space, hence the dependence of w(z) on z. Due to diffraction, a Gaussian beam will converge and diverge from an area called the beam waist (w0), which is where the beam diameter reaches a minimum value. The beam converges and diverges equally on both sides of the beam waist by the divergence angle θ (Figure 2). The beam waist and divergence angle are both measured from the axis and their relationship can be seen in Equation 2 and Equation 32:

Fixed lens camera focal lengths can also be multiplied by the crop factor of the sensor in order to compare it across formats. This is generally only important if you’re trying to replicate a look across focal lengths; i.e. you know you want a 135mm full-frame portrait style.

The wavefront of the laser is planar at the beam waist and approaches that shape again as the distance from the beam waist region increases. This occurs because the radius of curvature of the wavefront begins to approach infinity. The radius of curvature of the wavefront decreases from infinity at the beam waist to a minimum value at the Rayleigh range, and then returns to infinity when it is far away from the laser (Figure 3); this is true for both sides of the beam waist.3

The angle of view in photography is the area of the scene that is captured by the camera sensor. This area is described in degrees of coverage in front of the camera.

Hello Dan! I’m Mariam from Mauritius. I wanted to thank you for this deep explanation on focal length! I just bought my first camera and your article helped me so much!

Hopefully, this article on explaining focal length has clarified some of the stickier aspects of the topic. Especially where they affect wide, normal, and telephoto fields of view.

While we do go into some depth here and there are some confusing elements surrounding the topic, I’m confident that by the end of this article, you’ll have a solid foundation on what is focal length and how it relates to digital photography.

In many laser optics applications, the laser beam is assumed to be Gaussian with an irradiance profile that follows an ideal Gaussian distribution. All actual laser beams will have some deviation from ideal Gaussian behavior. The M2 factor, also known as the beam quality factor, compares the performance of a real laser beam with that of a diffraction-limited Gaussian beam.1 Gaussian irradiance profiles are symmetric around the center of the beam and decrease as the distance from the center of the beam perpendicular to the direction of propagation increases (Figure 1). This distribution is described by Equation 12:

By taking the crop factor of a specific sensor and multiplying it by the field of view, we get the field of view as if it were viewed in the 35mm standard.

There are great apps and websites that allow you to calculate depth of field for a given focal length, aperture, subject distance, and sensor.

Focal length and depth of field are different properties of both a lens and sensor but are somewhat related. Depth of field is how much of a scene is in sharp focus. How narrow or wide the depth of field is, is an interaction between focal length, sensor size, subject distance, and aperture value.

Focal length also relates to field of view (also called angle of view) because changing the focal length changes the field of view – I’ll explain more about how the field of view and focal length of a lens interact with each other in greater detail below.

Macro lenses have the highest magnification due to their unique construction, which reduces the focal distance they operate within and allow you to focus in very close subjects.

In the above equations, λ is the wavelength of the laser and θ is a far field approximation. Therefore, θ does not accurately represent the divergence of the beam near the beam waist, but it becomes more accurate as the distance away from the beam waist increases. As seen in Equation 3, a small beam waist results in a larger divergence angle, while a large beam waist results in a smaller divergence angle (or a more collimated beam). This explains why laser beam expanders can reduce beam divergence by increasing beam diameter.

Focal length is one of the main considerations when buying and selecting a lens. And understanding how focal length works is essential to capturing the photos you want. Otherwise, you’ll be choosing lenses with random angles of view that only serve to confuse you with choices.

Differentiating Equation 34 with respect to the focal length of the focusing lens (f) and solving for f when d⁄df [wL (f )] = 0 reveals the lens focal length resulting in the minimum beam radius, and therefore highest intensity, at the target.

By twisting the barrel of a zoom lens, you can adjust the focal length and field of view of your lens, which affects depth of field, distortion, and all other aspects of your image.

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These super long focal lengths are usually more expensive but they allow to capture subjects from a very far distance like in sports and wildlife photography, and to shoot other genres like deep astrophotography.

The total distance from the laser to the focused spot is calculated by adding the absolute value of s to s’. Equation 9 can also be written in a dimensionless form by multiplying both sides by f:

However, using a prime lens means that you have to physically move in order to create a given field of view. Which kind of lens is better is an age-old question and really comes down to your own personal preferences!

Focal length determines many of the characteristics of the photos you can take as well as the physical dimensions of the lens.

Gaussianlaser beam spot size

This equation approaches the standard thin lens equation as zR/f approaches 0, allowing the standard thin lens equation to be used for lenses with a long focal length. Equations 9 and 10 can be used to find the location of the beam waist after being imaged through the lens (Figure 5).

The simplest focal length definition is a description of the distance between the center of a lens and the image sensor when the lens is focused at infinity.

Apart from the definition of focal length in photography as the measurement in millimeters from the lens to the image sensor, focal length has a direct impact on the angle of view, which is a static property of the lens in question but is impacted by the sensor crop factor.

A plot of the normalized image distance (s’/f) versus the normalized object distance (s/f) shows the possible output waist locations at a given normalized Rayleigh range (zR/f) (Figure 6). This plot shows that Gaussian beams focused through a lens have a few key differences when compared to conventional thin lens imaging. Gaussian beam imaging has both minimum and maximum possible image distances, while conventional thin lens imaging does not. The maximum image distance of a refocused Gaussian beam occurs at an object distance of -(f + zR), as opposed to –f. The point on the plot where s/f is equal to -1 and s’/f is equal to 1 indicates that the output waist will be at the back focal point of the lens if the input is at the front focal point of a positive lens.

Focal distance is the distance between the subject you are focusing to the camera sensor. Lenses that can work at close focal distances have higher magnification (or reproduction ratios) relative to lenses that need you to stay far from the subject.

In practical terms, angle of view and field of view are used interchangeably in photography to indicate the way our cameras “see” the scene, and using a short focal length or a long focal length will change drastically the field of view or the amount of the scene that is photographed.

As |s| approaches either zero or infinity, d⁄df [wL (f )] = 0 when f = L. In both of these cases, the input beam is approximately collimated, and it thereby follows that the smallest beam radius would occur at the focal point of the lens.

Understanding your camera’s zoom ability helps you know what sort of pictures you can reasonably expect to take. Just like with an interchangeable lens camera (ILC), the camera will have a focal length range that tells you about the properties of the lens.

Spot sizeoflaser beamformula

Focal length differences are especially stark with wide-angle lenses. Each mm of width makes a visible difference, unlike telephoto lenses where it takes several mm to be easily noticeable.

Zoom lenses are what anyone who has ever picked up a camera in recent times is familiar with. In fact, they are so common that I often find non-photographers get baffled when I hand them a camera with a prime lens attached!

Counterintuitively, the intensity of a focused beam in a target at a fixed distance (L) away from the lens is not maximized when the waist is located at the target. The intensity on the target is actually maximized when the waist occurs at a location before the target (Figure 10). This phenomenon is known as Gaussian focal shift.

Laser beam spot sizecalculator

Standard lenses or medium focal lengths are suitable for shooting many different genres like portrait, street photography, landscape, etc.

One key to understanding focal length is recognizing how the look of the image changes using lenses with different focal lengths. Using a wide-angle lens, foreground elements are emphasized while background elements are pushed even further away, looking smaller than they really are.

The focused beam waist can be minimized by reducing the focal length of the lens and |s|-f. The terms next to w0 in Equation 17 are defined as another form of the magnification constant α in order to compare the values of the input beam to the output beam after going through the lens (Figure 8).3

Standard focal lengths range from 35mm to 50mm depending on the type of camera sensor. The field of view provided by standard focal lengths approximates the field of view of the human eye.

Can you help me understand why a lens advertised as 60 mm f2.8 macro is described as 120mm and equivalent to 35mm focal length? I am completely bewildered.

I emphasize that we get the field of view because again, lens focal length is inherent to a lens. A 25mm Micro 4/3rds lens has a 50mm full-frame field of view. However, it remains a 24mm lens with the distortion properties of a 24mm lens; it’s not magically a 50mm lens.