Why do Full Frame lenses and crop body lenses exhibit the same crop factor when used on a crop body camera?

Question

I have a Canon 7D, which has a crop factor of 1.6x.

When using a Canon EF-S lens I get the focal length stated on the lens, when using a Canon EF lens I get the focal length times 1.6 when used on the APS-C body. At least that's what I thought.

I just compared two lenses:

• Canon EF-S 15-85mm f3.5-5.6
• Canon EF 70-200mm f4

I took the same photo as you can see here.

The top photo is shot with the 15-85, the bottom photo with the 70-200 - both lenses are set to 70mm. Now why do they look the same?

I thought I would get 112-320mm (70mm*1.6 crop factor). What did I misunderstand about the crop factor calculation? Lightroom also displays the photos as having "70mm" and not 112mm.

Answer 1

Whether a lens is an EF or an EF-S lens, the actual focal length is always used. There are certain technical reasons why this is so, but the simplest is that a lens' focal length is defined as the distance from the film plane needed when the lens is focused at infinity to cast point light sources as a single point on the film plane. This doesn't change with regard to sensor size. What does change with regard to sensor size is the angle of view or field of view (FoV) that a lens of a specific focal length will include in the part of the image circle that falls on the sensor.

What this means is that if you are using a 70mm lens on a Full Frame camera, the FoV will be about 34° diagonally. The same 70mm lens on a crop sensor body will have an FoV of about 21°. That is an equivalent FoV of about a 110mm lens on the FF body, and that is why camera manufacturers say that the 70mm lens on a crop body is a 110mm equivalent. If you print photos taken of the same subject from the same distance using the same focal length lens with both cameras on the same size paper, the image from the crop sensor camera will make the subject appear larger. This is because the ratio between the crop sensor size and the print size is greater than the ratio between the larger full frame sensor and the same print size, thus the magnification factor of the photo taken with the crop sensor body is higher.

If you take both images shot at 70mm on your 7D with an EF 70-200mm f/4L and an EF-S 15-85mm f/3.5-5.6 IS they will have the same FoV because both lenses are set at 70mm. To understand the 35mm equivalent FoV they yield, both lenses need to be multiplied by the crop factor, even though one of the lenses does not project a light circle large enough to fill a full frame sensor.

Answer 2

The crop factor applies to all lenses shot on camera with a smaller sensor. They look the same because 70mm is 70mm on both lenses, and they're both cropped in exactly the same way.

I think the answers to Is an EF 50mm f/1.4 the same as 50mm with an EF-S lens on a Canon 550D? should help.

Also check out my answer to What is Angle of View?, because the concepts are closely related, the explanation for angle of view explains crop factor as well

A smaller sensor is literally like taking a photo from a larger sensor and cropping it. This has a number of advantages in certain situations: if you crop and enlarge, as long as you still have the detail, that's more zoom "for free"; also, the center of lenses tend to have better image quality. So, in situations where you want a lot of reach and are likely to crop anyway, using a crop-sensor body is cheaper and possibly faster and has no real drawbacks. Some people argue that the smaller pixels on crop sensors even give an advantage here; I think that's open for debate, and in fact it is debated under Are full-frame cameras bad for sports photography? and Is crop-factor a bad thing?

Answer 3

Crop factor isn't a measure of a lens, it's a measure of a sensor. The lens use the same measure, which is actually the focal length of the lens, or the distance the light travels as it is brought to a single point of focus. The reason it doesn't take a lens that long is that a compound lens can move the light around within it. Crop factor is useful for comparing the effective focal length for different camera bodies with different crop factors. For example, your shot using a 70mm lens on a camera with a 1.6 crop factor would require a 112mm lens on a camera with a crop factor of 1.

Answer 4

It is called a crop sensor camera, not a crop lens. The sensor is smaller, just as if you took the same image with a full frame camera and cropped it.

The lens does not know what kind of camera you are using. You could put a "crop sensor lens" on a APS-C, APS-H, FF or medium format camera, and it would still be the same. Put the OP's two lenses on each of these cameras, shoot at 70mm, and the lens still takes the same photo.

Answer 5

Easiest answer for the non technical: The lens does not provide the multiplication factor it is the sensor size of the camera. Setting both the lenses to 70mm are on the same size sensor (photo frame).

Projected onto a full size sensor both lenses would show similar results except the EF-S lens image may not give full sensor coverage (edges would be extremely poor/smaller image circle). NOTE EF-S lenses are not recommended for Full Frame incase they hit the mirror mechanism.

Answer 6

About crop factor: You should know that the camera lens acts just like a slide projector lens. The camera lens projects a miniature image of the outside world on a flat screen. This screen is the surface of film or digital chip. Now most of you know that long focal length lenses magnify; they present a telescopic view, so we call them telephoto. Conversely, short focal length lenses yield a wide-angle view. Now you should ask yourself, what focal length when mounted on my camera yields a “normal” view? In the vernacular of photography, “normal” translates to a view that delivers about the same perspective as the unaided human eye.

Now over the years the size of the camera has shrunk. This is due to advancements in film and digital imaging sensors. Consider that the lenses used on the giant cameras of the past would perform as super telephoto lenses if mounted on today’s miniature cameras. So what constitutes a “normal” lens?

Every camera lens projects a large circular image. Inside the camera are baffles and a mask. These shunt the peripherals of the circular image area allowing only the central part of the image to play on film or sensor. We need this masking because only the center of the circular projected image has sufficient definition to be pictorially useful. For the full frame 35mm (Fx) format the size of the circle must be about 50mm. For the compact digital (Dx) format, the size of the circle must be about 30mm. These values are approximately the diagonal measurement of the image mask (film or digital format rectangle).

When we mount a lens with a focal length about the same as the diagonal measure, it delivers a circle of good definition that completely covers the format rectangle right down to the corners. In other words we get almost no fall-off of image quality over the entire span. Additionally, when we mount a lens with a focal length about equal to the diagonal measure of the format, we get an angle of view of about 45⁰ with the camera held in the horizontal (landscape) position. The image delivered by such a lash-up replicates the human perspective.

Now the full frame 35mm format stems from about the 1930’s. This frame size measure 24mm height by 36mm length. The “normal” lens for this rectangle is by tradition 50mm. The actual value is about 43mm but opticians prefer to round this value up to 50mm. The modern compact digital stems from advances in chip making. It measures 16mm height by 24mm length. Thus it is 66% of the size of the full frame. Now 66% = 0.66 expressed as a decimal fraction and the inverse of this value is 1/0.66 = 1.5. What is this value 1.5? It tells us that the Fx is 1.5 times larger than the Dx. How do we use this value? A 30mm lens mounted on a Dx preforms like a 30 x 1.5 = 45mm mounted on a Fx. Or a 105mm mounted on a Fx preforms like a 105 ÷ 1.5 = 70mm mounted on a Dx.

Is this crop factor (magnification factor) useful? Yes if you are an old gray-hair like me who has used full frame cameras for years and has lots of used but good lenses for them. For you youths, the crop factor is more confusing than useful. Know what’s wide-angle – normal – telephoto for your format Otherwise you will be more confused when tomorrows even smaller digitals hit the market. For the record: Wide-angle is 70% or normal or shorter – telephoto is 200% of normal or longer.