Aperture Equivalent when using E-Nex lenses on Sony A7/7r

Shahrooz51

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Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
The focal length and the aperture are what are painted on the lens. They do't change if you use a different camera annd no camera at all. They are the physical properties of the objective.

If you want to think in "full frame equivalences" which may be useful for comparison purpouses (not really for much else), then you adjust everything by the crop factor.

(btw, it helps if you don't write f4 or f6, but f/4 and f/6. the f stands for focal length and the aperture is focal length divided by an aperture number, for example on 50mm f/2 lens the maximum aperture is 25mm.)
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?
Honestly, I don't know why you would want to invest in a full-frame camera to use crop lenses on it. I could understand if you already have an investment in those lenses but not because you perceive a lack of lenses for a system that's not even a year old.

I have the 24-70/4, 55/1.8 and 70-200/4. This covers just about everything I need and most of what I want. Let's assume that the 16-35/4 and (possibly) a G macro and 85/1.8 are coming at Photokina. What else do you think is missing?
 
So...what happens when you have a full frame image, then crop to an APSC size image?

--
Film is a four letter word
This is an interesting question and is one of the reason people may be confused. I hope I understand what you mean.

Even if you use a scissor, you may think that the dof and noise will remain unchanged. Just because the image is the same. But the logic is wrong.

If you have a smaller image, you will have to go closer to view it. Some parts which were sharp when viewing the uncropped image may appear unsharp. In the same way, the noise will appear more visible.
And thus you should see the flaw in your argument about exposure equivalence. The noise at detail level is the same. The reason you see more noise is due to enlargement effect. Hence, f/4 is f/4 for exposure, regardless of crop factor.
If you use full frame (FF) and APS-C at f/4, 1/1000s, and same ambient light, then the full frame collects about 2.25 times more light. Since noise is almost entirely a function of captured light, the image taken with larger sensor with the same exposure will have less noise.

As a thought example, let's say we have FF and APS-C with 24MP and cameras with similar tehnology level. The FF will have about 2.25 times larger fulll well capacity and at the same exposure it will collect about 2.25 times more light. Let's say the APS-C collects 10.000 photons per pixel and the FF callects 22.500 photons per pixel. We can safely ignore read noise as it's irrelvant at an exposure of this amount. The APS-C will have noise of sqrt(10.000) = 100 photoelectrons, the FF sqrt(22.500) = 150 photoelectrons. But since the noise we think of is actually signal-to-noise-ratio (SNR), not the absolute noise, the APS-C pixel in this case would have SNR of 10.000/100 = 100, while the FF 22.500/150 = 150, thus the FF image has much less noise.

You said - f/4 is f/4 for exposure. This is of course true. But it is quite a meaningless statement. You might just as well say that 1/1000s is 1/1000s for exposure or that illuminance of 100 lux is illuminace of 100 lux for exposure.

What is important is the effect of the aperture in the relevant formats. A cell phone camera at f/4 creates a very different image from a medium format camera using the same exposure parameters.
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
An example:
  • A 50mm lens is a 50mm lens on a FF camera or an APS-C camera. It is what is, a 50mm focal length (FL) lens. The FL doesn't change when you switch cameras with different sensor sizes.
  • Field of View (FOV) does change with sensor size. A 50mm FL lens on FF camera has a 46.6° diagonal FOV. A 50mm on an APS-C camera has a 31.5° diagonal FOV, hence the reason we call it cropped. If you use the Cropped mode on the a7r, then a 50mm FL lens will have approximately the same FOV as it would on an APS-C camera.
  • A lens aperture value is given in FF equivalent value, so a f/2.8 will be f/2.8 on a FF a7r as long as you don't use cropped mode. A f/2.8 on an APS-C camera will be equivalent to f/4. Figure approximately 1 full stop of aperture faster on a FF sensor than on an APS-C sensor, assuming you don't crop the sensor.
  • DOF will be greater on a FF sensor than on an APS-C sensor, assuming you don't crop the sensor.
There are reports of some E mount APS-C lenses that work without cropping on the a7x series. None of my lenses do, but I've read that some FLs for the 10-18mm zoom work without cropping.

--
An astrophotography hobbyist and amateur radio instructor and examiner. Sony a7, Sony a6000, and Canon Powershot G1 X. https://www.flickr.com/photos/jackswinden/
 
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So...what happens when you have a full frame image, then crop to an APSC size image?

--
Film is a four letter word
This is an interesting question and is one of the reason people may be confused. I hope I understand what you mean.

Even if you use a scissor, you may think that the dof and noise will remain unchanged. Just because the image is the same. But the logic is wrong.

If you have a smaller image, you will have to go closer to view it. Some parts which were sharp when viewing the uncropped image may appear unsharp. In the same way, the noise will appear more visible.
And thus you should see the flaw in your argument about exposure equivalence. The noise at detail level is the same. The reason you see more noise is due to enlargement effect. Hence, f/4 is f/4 for exposure, regardless of crop factor.
If you use full frame (FF) and APS-C at f/4, 1/1000s, and same ambient light, then the full frame collects about 2.25 times more light. Since noise is almost entirely a function of captured light, the image taken with larger sensor with the same exposure will have less noise.

As a thought example, let's say we have FF and APS-C with 24MP and cameras with similar tehnology level. The FF will have about 2.25 times larger fulll well capacity and at the same exposure it will collect about 2.25 times more light. Let's say the APS-C collects 10.000 photons per pixel and the FF callects 22.500 photons per pixel. We can safely ignore read noise as it's irrelvant at an exposure of this amount. The APS-C will have noise of sqrt(10.000) = 100 photoelectrons, the FF sqrt(22.500) = 150 photoelectrons. But since the noise we think of is actually signal-to-noise-ratio (SNR), not the absolute noise, the APS-C pixel in this case would have SNR of 10.000/100 = 100, while the FF 22.500/150 = 150, thus the FF image has much less noise.

You said - f/4 is f/4 for exposure. This is of course true. But it is quite a meaningless statement. You might just as well say that 1/1000s is 1/1000s for exposure or that illuminance of 100 lux is illuminace of 100 lux for exposure.

What is important is the effect of the aperture in the relevant formats. A cell phone camera at f/4 creates a very different image from a medium format camera using the same exposure parameters.
I think a lot of people get stuck on the numbers, especially since they want to believe that their APS-C camera is every bit as good as full-frame. They say things like "f/4 is f/4", and it is but we're not talking about exact numbers, we're talking about equivalent results.
 
Assume you have an f = 50 mm focal length lens, any such lens, for a cell phone to medium format. Then f/4 means that the aperture is open to 50/4 mm = 12.5 mm diameter. And that does not depend on what kind of format sensor/film/ … follows the lens.

The lens allows a 12.5 mm diameter circle of light to pass through.

How does it suddenly become f/6 when you use the lens in crop mode on an A7?

Apparent depth of field changes for an equivalent sized image.

So please be careful with simple fractions in optics like f/4, fractions from 6th grade. You are only fooling yourself.
I said shooting f4 with an APS-C is equivalent to shooting f6 with FF in terms of resulting image.
No, it is not. The resulting image isn't only about FOV and DOF. It is also about exposure values, and resulting brightness of the image relative to the scene.
I never said f4 would become f6 !!! Please do not change what I am saying.
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?
No. Your maximum aperture (not the lowest) will be f/4 regardless of the sensor size used.

The idea of equivalence is merely to compare field of view (FOV) and depth of field (DOF). The 18-105mm is an APS-c lens that provides a FOV range that you will get if you used 28-160mm lens on FF camera. In other words, if you use 18mm focal length to capture an image with a6000 (APSc), you would need 28mm focal length on a7 (FF) for the same field of view.

The next argument is about DOF. At 18mm f/4, you get a specific depth of field on a6000. This will be similar to depth of field you'd get using 28mm f/6 setting on a7. So, f/4 doesn't become f/6. In fact, the crop factor simply equalizes an 18/4 on APSc to 28/6 on FF... and you get same FOV and DOF.

Finally, and this is where many mess up, your exposure values are going to be the same on APSc as they would be on FF, implying f/4 is f/4. In other words, if you use 1/1000s, f/4 at ISO 100 on a6000 for a specific scene, you would also be using 1/1000s, f/4 at ISO 100 on a7 (instead of 1/1000s, f/6 at ISO 100 on a7... which will result in underexposure compared to the f/4 setting by 1.5x).
 
Do you realize you will only achieve about 10-12 mp by using an APSC-designed lens on the A7?
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
I've read only few replies, haven't read all of them, so it might be somebody already provided a correct explanation.

And the explanation if actually very simple. You need to multiply by a crop factor the FL and the f-stop to arrive to equivalent lens. So if you mount 18-105mm f/4 on your A7r in crop mode it will be equivalent to a 27-157.5mm f/6 FF lens -- meaning both of those lenses would result in the same FOV, DOF, shot noise, and since it's the same sensor the read noise will also be the same. So you get pretty much identical results with both lenses with the exception of the resolution, low ISO dynamic range, and some other less important factors.

P.S. beware, the 18mm on that lens is closer to 20mm in reality.
 
Equivalent with respect to what?

This whole argument seems to revolve around the fact that some people are making an assumption that the others aren't.

Specifically, many people are assuming that the images are viewed/printed at the same physical size, while others are talking about the image at the sensor.

Clearly, as the lightmeter example makes clear, sensor size does not affect exposure and the f value remains the f ratio of lens aperture to focal length, which specifies how much light reaches the sensor per unit time. Another example would be a poorly synched flash picture, where the sensor is only partially uncovered when the flash fires. The result (believe me, I have done this often enough) is a perfectly exposed image on half the sensor. There is no way for a pixel to know how many other pixels there are - it only responds to the light that hits it.

Once you start talking about DOF, there is an argument to be made, even though I don't understand it mathematically.

Once you start magnifying images different amounts to get a specific print size, it gets complicated, but, at the sensor image level, for exposure purposes (not DOF), equivalent f stop is not a useful concept.

Mike
 
Equivalent with respect to what?

This whole argument seems to revolve around the fact that some people are making an assumption that the others aren't.

Specifically, many people are assuming that the images are viewed/printed at the same physical size, while others are talking about the image at the sensor.

Clearly, as the lightmeter example makes clear, sensor size does not affect exposure and the f value remains the f ratio of lens aperture to focal length, which specifies how much light reaches the sensor per unit time. Another example would be a poorly synched flash picture, where the sensor is only partially uncovered when the flash fires. The result (believe me, I have done this often enough) is a perfectly exposed image on half the sensor. There is no way for a pixel to know how many other pixels there are - it only responds to the light that hits it.

Once you start talking about DOF, there is an argument to be made, even though I don't understand it mathematically.

Once you start magnifying images different amounts to get a specific print size, it gets complicated, but, at the sensor image level, for exposure purposes (not DOF), equivalent f stop is not a useful concept.

Mike
Amen!

Although, the issue mainly comes from resistance to fact that noise is not any different, just more visible from smaller sensors due to need for greater enlargement to same print/viewing size... and promotion that it is because of more light gathering on FF (which, ironically, they fail to realize REQUIRES more light for same exposure). But, they happen to take the popular route, and repeating it enough has led to that belief, of f-stop not being f-stop for exposure values rather than some kind of equivalence.
 
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There are two characteristics inferred by the f/ number of a lens, the aperture and how much light it lets in, and the depth of field at a given distance.

The first is rather fixed. A calculation based on the actual focal length. F/4 is f/4 and will allow in the same amount of light regardless of focal length, equivalent focal length, or sensor size etc. (minor fluctuations can happen due to rounding values or lens coatings, but these are negligible).

Then you have depth of field and how blurry the back ground is. At the same distance and aperture, a lens on FF and a lens on APSC will have the same back ground blurriness. However, since the APSC has a smaller crop, you will need to back the camera up to achieve the same composition. The backing of the camera will increase the depth of field, as DoF is a function of lens to subject distance.

Alternatively, you can keep the same composition by using a wider lens on the APSC camera. DoF will increase as it is also a function of focal length.

So "f/4" is a descriptor in light gathering properties more than a descriptor in DoF as DoF will change with sensor size (and always has, even back in film, not just with APSC sensors).

You can say, however, the depth of field equivalence of a lens on APSC is 1.5 times that of FF, if you keep the composition the same. This is far different than saying an f/4 lens is an f/5.6 lens on APSC, which is mathematically and empirically incorrect.
Agreed.
 
There are two characteristics inferred by the f/ number of a lens, the aperture and how much light it lets in, and the depth of field at a given distance.

The first is rather fixed. A calculation based on the actual focal length. F/4 is f/4 and will allow in the same amount of light regardless of focal length, equivalent focal length, or sensor size etc. (minor fluctuations can happen due to rounding values or lens coatings, but these are negligible).

Then you have depth of field and how blurry the back ground is. At the same distance and aperture, a lens on FF and a lens on APSC will have the same back ground blurriness. However, since the APSC has a smaller crop, you will need to back the camera up to achieve the same composition. The backing of the camera will increase the depth of field, as DoF is a function of lens to subject distance.

Alternatively, you can keep the same composition by using a wider lens on the APSC camera. DoF will increase as it is also a function of focal length.

So "f/4" is a descriptor in light gathering properties more than a descriptor in DoF as DoF will change with sensor size (and always has, even back in film, not just with APSC sensors).

You can say, however, the depth of field equivalence of a lens on APSC is 1.5 times that of FF, if you keep the composition the same. This is far different than saying an f/4 lens is an f/5.6 lens on APSC, which is mathematically and empirically incorrect.
Agreed.
--
Film is a four letter word
f4 on APS-C is equivalent to f6 on FF in terms of dof AND light.
Nope
The equivalent aperture not only tells you how much depth-of-field you get, on a different system, it also tells you how much total light you'll get.
.
What is important (for the final resulting image) is the total light collected on the sensor.
The total amount of light for a given area, not the total, or else cropping in post will change the exposure at the time of capture.

The properties of the lens don't change when the sensor size changes.
In equivalent settings, the total light is the same ( and thus the same noise).

So, equivalent aperture (with equivalent settings) give the same results in nearly every aspect !!!!
--
I don't have any AF lenses, so if I want a picture, I have to do more than squeeze a button.
http://www.flickr.com/photos/lightshow-photography/
My lenses:
http://www.fredmiranda.com/forum/viewprofile.php?Action=viewprofile&username=LightShow
 
The sensor size has a big impact on the light received by the sensor.
The extra light around the edges gives you a bigger picture covering a wider angle. (Assuming the lens can cover.)
Whatever your light meter says, the bigger sensor recieves much more light when shooting with the same f-number !
But it receives the same the same illuminance (light per square mm), so the exposure is the same.
 
If you use full frame (FF) and APS-C at f/4, 1/1000s, and same ambient light, then the full frame collects about 2.25 times more light. Since noise is almost entirely a function of captured light, the image taken with larger sensor with the same exposure will have less noise.
If it is printed to the same size, yes; because the degree of enlargement is less.

As for shot noise, that depends (mainly) on the size of the pixels. So it will be less if the number of pixels on a FF sensor is less than twice the number on a sensor of half the area.
As a thought example, let's say we have FF and APS-C with 24MP and cameras with similar tehnology level. The FF will have about 2.25 times larger fulll well capacity and at the same exposure it will collect about 2.25 times more light. Let's say the APS-C collects 10.000 photons per pixel and the FF callects 22.500 photons per pixel. We can safely ignore read noise as it's irrelvant at an exposure of this amount. The APS-C will have noise of sqrt(10.000) = 100 photoelectrons, the FF sqrt(22.500) = 150 photoelectrons. But since the noise we think of is actually signal-to-noise-ratio (SNR), not the absolute noise, the APS-C pixel in this case would have SNR of 10.000/100 = 100, while the FF 22.500/150 = 150, thus the FF image has much less noise.

You said - f/4 is f/4 for exposure. This is of course true. But it is quite a meaningless statement. You might just as well say that 1/1000s is 1/1000s for exposure or that illuminance of 100 lux is illuminace of 100 lux for exposure.

What is important is the effect of the aperture in the relevant formats. A cell phone camera at f/4 creates a very different image from a medium format camera using the same exposure parameters.
In bright light, if they both have 16 Megapixels, the images will be much the same. The difference shows in dimmer light, where the small pixels suffer more from shot noise.
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
An example:
  • A 50mm lens is a 50mm lens on a FF camera or an APS-C camera. It is what is, a 50mm focal length (FL) lens. The FL doesn't change when you switch cameras with different sensor sizes.
  • Field of View (FOV) does change with sensor size. A 50mm FL lens on FF camera has a 46.6° diagonal FOV. A 50mm on an APS-C camera has a 31.5° diagonal FOV, hence the reason we call it cropped. If you use the Cropped mode on the a7r, then a 50mm FL lens will have approximately the same FOV as it would on an APS-C camera.
  • A lens aperture value is given in FF equivalent value,
No, it is a simple ratio of focal length to diameter of aperture. The sensor size has no effect on it.
  • so a f/2.8 will be f/2.8 on a FF a7r as long as you don't use cropped mode. A f/2.8 on an APS-C camera will be equivalent to f/4. Figure approximately 1 full stop of aperture faster on a FF sensor than on an APS-C sensor, assuming you don't crop the sensor.
No, it will not. Take a lens off a FF camera such as the A7, and put it on an A6000 without changing the aperture or focus, and the same shutter speed (and ISO) will give you the exact same picture. Just with the edges missing.
  • DOF will be greater on a FF sensor than on an APS-C sensor, assuming you don't crop the sensor.
Not if you keep the aperture the same. The DoF in the image on the sensor remains unchanged. However, if you enlarge either photo more than the other, it will have less DoF, because you make the blur bigger.
 
f4 on APS-C is equivalent to f6 on FF in terms of dof AND light.

What is important (for the final resulting image) is the total light collected on the sensor. In equivalent settings, the total light is the same ( and thus the same noise).

So, equivalent aperture (with equivalent settings) give the same results in nearly every aspect !!!!
Possibly your comment is lost in translation, but note that if your point was true, someone should tell Sekonic et al as no light meter ever made has demanded to know what size sensor (or format of film) you were using to determine exposure.
You need to ask yourself a few questions:

1) what does your Sekonic measure?

2) does your Sekonic tell you the noise or DOF you are going to get at those settings?

3) are the pictures that you take with cameras with different size sensors or different crops based on the same Sekonic reading going to look the same?

I think you need to read first before arguing, because contrary to popular opinion on this forum, ignorance is not a bliss.

How about this introductory article written by DPR staff?
 
So...what happens when you have a full frame image, then crop to an APSC size image?
Why? -- Exactly the same, of course.

It doesn't matter how you change the crop factor (smaller sensor, crop in PP, teleconverter, focal reducer) -- the result is the same, because what matters is the area that the light is collected from.

I think what people miss in this discussions is that the lens equivalence assumes viewing equivalence: you want to have the same FOV, DOF, noise, and the same final image size.
 
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
It is hidden in thread somewhere, but here are the main points:

Aperture is a LENS property. It is defined as the focal length (FL) divided by its maximum aperture (AE). This is unrelated to sensors (or even camera types).

Exposure is also regardless of sensors. f/4, ISO 400, 1/100th is the SAME exposure on all cameras, from your cell phone to your medium format and beyond.

This is why light-meters work - they simply tell you proper settings based on measured light (and method).

So, if all sensors expose the same - do they all receive the same amount of light?

Yes, on a per measurement of area basis. (Typically not pixel, because pixel sites are not the same size). But on a TOTAL AREA basis, a larger sensor receives more light, given the SAME exposure.

Of course, a larger sensor which uses the same exposure settings will have less noise (because of more light) and less DOF (because of less enlargement for viewing full image).

Now, to make the larger sensor equivalent to the smaller sensor, you have to add noise (higher ISO) and add DOF (smaller aperture). As the formulas work, this goes together with the crop factor.

So, if I expose equal between APS-C and FF, FF will have less DOF and less noise.

If I expose equivalent between APS-C and FF, both will have same DOF and same noise.

In the spirit of the latter, speaking to the OP's question, yes, you would capture with f/6 on the FF (1.5x) when comparing to f/4 on the APS-C. You would also shoot at (just over) double the ISO (1 stop) the match the equivalent exposure (same DOF, same noise) (which then makes the exposure - i.e. light per area - the same again).

Of course, you don't have to. Using the equal exposure is perfectly fine, except that the FF image will show less DOF and less noise.

(I am assuming equivalent FOV - the FL also is subject to the crop, and this could change the light input. If the same FOV, this is a constant).
 
B.t.w., there is an interesting and very practical corollary of the lens equivalence:

* you can convert an FF lens to its equivalent APS-C lens by using a 1.5x focal reducer -- that's perhaps everybody knows;

* what's less known, you can do the opposite as well, you can convert an APS-C lens to its equivalent FF lens by using a 1.5x teleconverter.

So if you take your 18-105mm f/4 APS-C lens and attach a 1.5x teleconverter, you'll end up with a 27-157.5mm f/6 FF lens. You no longer need to use the crop on your A7R, the lens will cover the full frame. Now, why would you do that if you end up with the equivalent image: the same FOV, DOF, noise? -- There are advantages nonetheless: you get more pixels, and you get a better dynamic range at the base ISO.
Hi,

I have a A7r,it is really impressive camera. Because of lake of FE lenses,I want to buy E-mount (NEX) lenses and use with my A7r while I am aware of their crop factors.Also,I have read some articles about equivalent focal length and aperture value when we have crop sensor.My question is if we use E-Nex lenses on A7/7r camera do we have equivalent aperture too? For example,If I use a 18-105 mm f4 on my A7r,my lowest aperture will be f6?

Thank You.
I've read only few replies, haven't read all of them, so it might be somebody already provided a correct explanation.

And the explanation if actually very simple. You need to multiply by a crop factor the FL and the f-stop to arrive to equivalent lens. So if you mount 18-105mm f/4 on your A7r in crop mode it will be equivalent to a 27-157.5mm f/6 FF lens -- meaning both of those lenses would result in the same FOV, DOF, shot noise, and since it's the same sensor the read noise will also be the same. So you get pretty much identical results with both lenses with the exception of the resolution, low ISO dynamic range, and some other less important factors.

P.S. beware, the 18mm on that lens is closer to 20mm in reality.
 

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