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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?

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See also photo.stackexchange.com/questions/10079/… –  mattdm Apr 1 '11 at 20:34

6 Answers 6

up vote 19 down vote accepted

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.

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I think I instinctively knew that, but the concept was bugging the back of the brain enough for me to decide to post the question and see if I was just mentally missing something in the morning. –  John Cavan Jul 27 '10 at 14:33
6  
Sometimes I've believed as many as six impossible things before breakfast. –  Eruditass Jul 27 '10 at 23:08
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Sounds like a Douglas Adams quote, Eru. –  Nick Bedford Dec 6 '10 at 3:43
    
Things to do before going out for breakfast: Open a bank account with a balance of 0.01, pack your towel, and -- most importantly -- don't panic. –  anon Nov 26 '11 at 4:49

f/1.4 is faster by about 2/3rd of a stop than f/1.8. This is calculated pi*(focal-length/ f-stop/2)^2

50mm f/1.8 gives about 606mm² of light 50mm f/1.4 gives about 1000mm² of light

It does not affect the image on the sensor, merely the size of the cone of light from a single light source (of which your entire scene is filled with).

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Thanks Nick, I was sleepy that day, hence the question... I just updated the original because somebody decided that there was no such beast as a 50mm f/1.7 and changed it to a 50mm f/1.8. However, Pentax definitely produced an f/1.7... –  John Cavan Dec 6 '10 at 3:59
    
Yeah some "uncommon" lens have definitely been made. I've heard mention of an f/1.7 before. –  Nick Bedford Dec 6 '10 at 4:02
    
Since most of that is constant when comparing the two, you don't really need to use it. You can just compare the inverse of the f/stops squared. (1/focal-length)^2. Or, another way of thinking about it: you can compare the stops by taking log base sqrt(2) of the aperture to get the stop number.... f/1.4 is stop #1, and f/1.8 is stop #1.7. And f/1.7 is stop #1.5 — nicely halfway between f1/4 and f/2. (In all cases, highly rounded because the real world lenses don't reflect a high degree of precision here anyway.) –  mattdm Dec 6 '10 at 15:35
    
I often wonder whether f/1.2 lenses are actually half a stop faster than f/1.4 lenses or a third of a stop faster. It could be either (or anywhere in between!) depending on how the figures are rounded! –  Matt Grum Dec 6 '10 at 19:07
    
Well it yields 1.36x more light, so I guess it's 1/3rd stop brighter. –  Nick Bedford Dec 8 '10 at 2:07

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.

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But when you enlarge that crop to the same viewing size as the photo was before you cropped it you do reduce the depth of field. –  Michael Clark Jan 5 at 15:07

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.

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f/1.8 is quite fast, though obviously not the fastest. –  Nick Bedford Dec 6 '10 at 3:45

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.

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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.

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