Does lens speed still increase meaningfully when the physical aperture is larger than the sensor size?

Question

This question came to me this morning, thinking about 50mm lenses. I have the Pentax 50mm f/1.7 (manual) and it's a very nice lens, but would be considered (relatively) slow on 35mm film, and many recommendations would be for a 50mm f/1.4.

However, doing the math, the diameter of the f/1.7 aperture wide open is 29.4mm, which is greater than the diagonal size of an APS-C sensor — effectively meaning that no part of the sensor is "hidden" by the aperture. So, the questions is, does this actually have any meaning, or is the f/1.4 lens still going to be distinctly faster for APS-C?

Answer 1

f1.4 will always be 2/3rds stops faster than f1.8.

The diameter has nothing to do with whether or not part of the sensor is hidden. That is a separate measurement referred to as vignetting, and not the image circle's light level. The image circle's light level/brightness is directly affected by the aperture of the lens design.

FF lens simply means the image circle is designed to cover a full frame sensor (which can be film). Using it on a APS-C will be using the inner part of the image circlce.

An APS-C lens of the same focal length and speed could have been created at a smaller size the image circle does not need to be as large, but the lens would need to be redesigned.

Also, note that the Pentax 50mm f1.7 (if this is what you have) is generally regarded as sharper and/or more contrasty than the Pentax 50mm f1.4 at common apertures up until f2.8 or so.

Pentax 50mm f1.4 advantages include one third f-stop faster, rounder aperture blades for rounder highlight bokeh only when stopped down. It may or may not have "better" and smoother bokeh as that is not simply a function of aperture blades and I have not seen any other comparisons.

Answer 2

The max aperture has nothing to do with the sensor size.

The lens has a max sensor size that it can be used with, but that is because other elements limit the image circle, like the size of the front lens. (A fish eye lens may even have an image circle smaller than the sensor, leaving the corners black.)

The 1.8 lens isn't so slow. A zoom lens in the same price segment is about two stops slower, and they are not considered unusable. The 1.4 is faster, so it's just a question about what you need.

Answer 3

Does the sensor size really affect the depth of field though?

The full frame image would have a shallower depth of field, because to achieve the same framing, you can be closer to the subject thus having a shorter focusing distance, therefore shallower depth of field.

The amount of bokeh in the image would be the same for the same focusing distance, all the smaller sensor is doing is cropping. If I take a photo, crop the middle of it in Photoshop, I don't get more bokeh.

Answer 4

That people would recommend the f/1,4 over the f/1,8 for speed reasons is not related to the sensor size. The f/1,4 lens is simply faster than the f/1,8 (as discussed here) regardless of the size of the sensor.

However, a smaller sensor results in a greater depth of field at a given aperture. For this reason it could make sense to recommend a larger-aperture lens for a smaller sensor.

Answer 5

Assuming both the lenses cast light circles at least large enough to cover the entire sensor, an f/1.4 lens will always be faster than an f/1.7 lens by almost one half stop.

The aperture size has nothing to do with the size of the image circle a lens casts. The elements of a lens behind the aperture diaphragm and how much they bend the light allowed through the aperture are what determines the size of the image circle.

Consider this example: A Canon EF 600mm f/4 L IS II lens has an entrance pupil (effective aperture) 150mm in diameter. The back elements of the lens concentrate that light into a 44mm diameter image circle. If you stop that lens down to f/16, the size of the entrance pupil is reduced to 37.5mm in diameter. Yet that light is still spread over a 44mm image circle by the back elements of the lens.

Answer 6

As others have said, the f/1.4 lens will always be faster than the f/1.8 lens. I think the simplest example I can give to this is to imagine, say, a 400mm f/2.8 lens. That would have an aperture of about 140mm diameter, by my reckoning at least. That's plenty bigger than even full-frame D-SLRs.

Answer 7

ƒ/1.4 is brighter than ƒ/1.7 by roughly ⅔ stops. The equation to calculate the area of each lens aperture is:

50mm ƒ/1.7 gives about 679mm² of area
50mm ƒ/1.4 gives about 1002mm² of area

It does not affect the crop off the image, merely the volume of the cone of light from a single light source (of which your entire scene is filled with). Think of it as increasing volume of each cone of light the larger the aperture gets. The larger the aperture, the more photons can travel through the lens and focus onto the sensor at the same point.

That's why a smaller aperture will result in smaller circles of confusion (that are not focused on the sensor plane). It's not the position on the capture medium, but the width of the cone of light that changes according to the aperture.