Pentax 67 lens on a 35 mm Canon

[sanzari]

Reaching out to the scientists among us. What is the formula for calculating a field of view os a 45mm or 100mm Pentax 67 lens on a 35mm on a DSLR please.

Secondly if I shifted these lenses and stitched two images together how would the formula adapt to tell me the cropped field of view in 35mm language.

Am I making sense ? Thanks to the smart photags on this one

T

[RawheaD]

No math needed. A 45mm lens is a 45mm lens regardless of what camera you put it on.  So it will be like any other 45mm lens you can get to put on your 35mm DSLR. Slightly wider than a 50mm standard lens.

[ondebanks]

There is a universal formula for this:

angular field of view = 2 * arctan(sensor dimension/(2 * focal length))

...where sensor (or film) dimension is usually the diagonal distance from corner to corner. But the horizontal and vertical dimensions can be used for their respective angles too.
...arctan is arc-tangent aka inverse tangent (tan^-1 on a calculator)

You can pop this into an Excel spreadsheet as follows:

Column A, cell A1 = Sensor Dimension value
Column B, cell B1 = Focal Length value
Column C, cell C1 = FOV...enter the formula "=DEGREES(2*ATAN(A1/(2*B1)))"

...ATAN is arctan in units of radians...so the DEGREES() function converts this to degrees.

As I said, it's universal - any optic, any capture medium, any format size. Works just as well for the Hubble Space Telescope's Advanced Camera for Surveys as it does for a cellphone camera. I leave those calculations as an exercise...!

Ray

[Dick Roadnight]

No math needed. A 45mm lens is a 45mm lens regardless of what camera you put it on.  So it will be like any other 45mm lens you can get to put on your 35mm DSLR. Slightly wider than a 50mm standard lens.

The angle of view of a lens is the same for any format, but the format "angular field of view" is as above.

My 47mm lens is a 100 degree (lens angle of view) lens, with a 113mm image circle diameter, but I have to shift to use the image circle.  

[Dick Roadnight]

There is a universal formula for this:

angular field of view = 2 * arctan(sensor dimension/(2 * focal length))

...where sensor (or film) dimension is usually the diagonal distance from corner to corner. But the horizontal and vertical dimensions can be used for their respective angles too.
...arctan is arc-tangent aka inverse tangent (tan^-1 on a calculator)

You can pop this into an Excel spreadsheet as follows:

Column A, cell A1 = Sensor Dimension value
Column B, cell B1 = Focal Length value
Column C, cell C1 = FOV...enter the formula "=DEGREES(2*ATAN(A1/(2*B1)))"

...ATAN is arctan in units of radians...so the DEGREES() function converts this to degrees.

As I said, it's universal - any optic, any capture medium, any format size. Works just as well for the Hubble Space Telescope's Advanced Camera for Surveys as it does for a cellphone camera. I leave those calculations as an exercise...!

Ray

Yes, I think I have that formula in a spread sheet on my phone.

...but the format angular field of view is the (angle subtended by) the format at the focal length... so, if you are using a 640mm lens on a micro 4/3, the format angle of view is about a thumb's width at arm's length.

...and you can double the numbers and hold you thumb and fore-finger 72mm apart 200mm from you eye for a 100mm lens on a 36mm mm sensor, (as 35mm format is 24 * 36mm).

If you shift and stitch you change the effective format, so, if you shift in the 36mm direction by 14mm, you would have a format width of 50mm, but the mirror box and throat of the 35mm camera might prevent you being able to do it. ...this is one nice thing about MF technical|view cameras - there is no mirror box to get tin the way.

[ondebanks]

My 47mm lens is a 100 degree (angle of view) lens, with a 113mm image circle of confusion, but I have to shift to use the image circle. 

Dick, I think you are doing Schneider an injustice!  I know you meant 113mm circle of coverage...the circle of confusion is something else, measured in microns not mm...

Ray

[Dick Roadnight]

Dick, I think you are doing Schneider an injustice!   I know you meant 113mm circle of coverage...the circle of confusion is something else, measured in microns not mm...

Ray

Yes, thank-you for the correction, I will edit my post, they call it the "image circle diameter" in Schneider.

[sanzari]

Wow I knew there was scientists here and boy did I get what I deserved.

I am more confused now than before. Let's keep it simple for me as the results I got I think we're correct so I asked the wrong question.

45 = 51
100= 24
300 = 8.3

Given the diagonal of the sensor is 43.3mm

I think these are angles of view ?

What I wanted to know was if I use the Pentax 67 lenses above on the 35mm camera what is the effective focal length on the 35mm?

Is that a different formula?

Thanks guys of course if I stitch two together I assume this halves the lens value as the angle doubles ?

Thanks again

[ondebanks]

Wow I knew there was scientists here and boy did I get what I deserved.

Hey, we're here to educate, not to punish 

I am more confused now than before. Let's keep it simple for me as the results I got I think we're correct so I asked the wrong question.

45 = 51
100= 24
300 = 8.3

Given the diagonal of the sensor is 43.3mm

I think these are angles of view ?

Yup, they look right.

What I wanted to know was if I use the Pentax 67 lenses above on the 35mm camera what is the effective focal length on the 35mm?

Is that a different formula?

If you're confused by the maths, my tip would be: when you are adapting a lens down to a smaller format, just forget where the lens came from and what format it is normally used on. Empty your mind of all thoughts of crop factors and "effective" focal lengths. Just look at the focal length printed on the lens. That is all that matters. It's the great leveller.

So a 45mm Pentax 67 lens is exactly the same as a 45mm DSLR/35mm lens. What's the focal length? 45mm. What's the effective focal length? 45mm. What's the crop factor? From the point of view of the DSLR/35mm camera, there is no cropping, so it's 1.0 - basically, fuggedaboudit.

45mm is not a common focal length, but DSLR manufacturers do make buckets of 50mm lenses and you may have one, so that tells you that the 45mm Pentax 67 lens is going to be very slightly wider, when used on a DSLR.

Thanks guys of course if I stitch two together I assume this halves the lens value as the angle doubles ?

You're not halving or changing the lens focal length at all in stitching - you're expanding the net angle of view alright, but how this is achieved is more analagous to expanding the sensor area. You are simulating a larger sensor, behind a lens with the same focal length but with a design that delivers larger angular coverage. (The angle projected by a lens is determined by its design, not by its focal length).

If we assume zero/minimal overlap between the stitched frames, then the field of view simply doubles in one direction, horizontal or vertical. It is unchanged in the other direction. Knowing these two numbers, you can use Pythagoras' theorem to work out the diagonal angle of view of the composite image.

Ray

[Dick Roadnight]

So a 45mm Pentax 67 lens is exactly the same as a 45mm DSLR/35mm lens. What's the focal length? 45mm. What's the effective focal length? 45mm.

I think that what he wanted to know, is what is the ff 35mm equivalent focal length?

Use the formula (or a web site) to calculate the format angle of view for the focal length and 67 sensor size, and then calculate the focal length for that format angle of view on a 35mm sensor.

For lenses of long focal length this will be approximately a simple ratio, but not for a 45 degree lens.

(The angle projected by a lens is determined by its design, not by its focal length).

The lens angular field of view is different to the format angle of view, and the image circle diameter must be bigger than the diagonal of the format to prevent corner clipping.

The lens projects a cone of light - the angle of the cone is the lens field of view... the base of the cone is the image circle (which gets bigger for higher magnification, i.e. greater extension). the focused image is the image circle, and the sensor (normally) captures part of it. (yes, you can get round images which are the whole image circle)

If we assume zero/minimal overlap between the stitched frames, then the field of view simply doubles in one direction, horizontal or vertical. It is unchanged in the other direction. Knowing these two numbers, you can use Pythagoras' theorem to work out the diagonal angle of view of the composite image.
Ray

Doubling the sensor size doubles the effect format size, and, for narrow angles of view, doubling the effective format size approximately doubles the angle of view... if your format angle of view is 90 degrees, you do not get 180 degrees by doubling the effective format size, but doubling the effective sensor size would double the subject field of view, but the subject field of view is not normally very relevant for landscape work (but it might be e.g. if you want to get a tree in the frame) but it is relevant if you are copying flat art work, or in the studio.

Pythagoras' theorem relates lengths of sides of a right angle triangle - nothing to do with angles. To calculate the format angle of view you need trigonometry - the formula quoted.
 

[ondebanks]

I think that what he wanted to know, is what is the ff 35mm equivalent focal length?

I don't think so. His question again: ...Pentax 67 lens on a 35mm or a DSLR. That's the question I answered.

Doubling the sensor size doubles the effect format size, and, for narrow angles of view, doubling the effective format size approximately doubles the angle of view... if your format angle of view is 90 degrees, you do not get 180 degrees by doubling the effective format size, but doubling the effective sensor size would double the subject field of view, but the subject field of view is not normally very relevant for landscape work (but it might be e.g. if you want to get a tree in the frame) but it is relevant if you are copying flat art work, or in the studio.

Pythagoras' theorem relates lengths of sides of a right angle triangle - nothing to do with angles. To calculate the format angle of view you need trigonometry - the formula quoted.

Yes indeed, but I was reverting to this rough planar approximation to spherical geometry, simply because the OP said he was struggling with my "proper" formula. It works reasonably well over small to modest fields of view, such as with the 100mm (I guess 105mm) lens he was proposing to use.

Things get more complicated again if you stitch not by shifting the lens, but by turning the camera to point in a different direction, as many photographers must do. Then you need a whole other, rather more complicated formula!

Ray

[sanzari]

This is getting awesome. I now understand every 3rd world makes me officially dumb in the 67 world..


So what I am trying to work out is when you put an 105 lens on a 67 Pentax it equates to putting a 50mm on a 35mm camera.

So if I put a Pentax 67 lens 45mm from what I read here is that it will be a 45mm ? Or will it be different?

Second question is then when I stitch two together using the 45mm lens what would be the effective focal length equivalent if I put a lens on the same 35 mm camera to achieve the same cropped ratio of adding 2 snaps together. ?

Is that any clearer.

Basically I want to explain to people that stitching two images together on a 35 mm using a Pentax 67 lens of focal length 45mm is better than using a single lens and cropping to the same field of view.

Equally 2 x 45mm 67 shots on a 35mm camera is better than taking an 80mm pixel MF camera cropping to a 3:1 ratio and what sort of lens focal length would I need it.

[Dick Roadnight]

Basically I want to explain to people that stitching two images together on a 35 mm using a Pentax 67 lens of focal length 45mm is better than using a single lens and cropping to the same field of view.

You can consider the long, short or diagonal format/film/sensor size and associated format angles of view... here you are considering increasing the actual long sensor size to an effective sensor size the same as the long size of the 67 film format?

So, the effective (long) format angle of view for the shifted 35mm sensor would be the same as the actual long format angle of view with the same lens on 67... same format size, same lens, same format angle of view. 

...but I am sure that the mirror box and throat of the 35mm camera would prevent you getting the full 70mm * 24mm image, and if it was possible you would have to use three images to get enough overlap for the merge software.

I have a Schneider Super Angulon 47xl 54 film lens which has a field of view of 120 degrees, so I might use it on my Sinar P2/3 when the 100 degree field of view of the Apo-Digitar 47xl is not enough, but I think this would push the Sinar to the limit on shift, even using e.g. front rise, rear fall, coarse tilt and an angled rail (the P3 converted from a P2 has more movement than the "proper" P3) but without a custom sliding back it would not be very practicable to try to stitch get a 5 inch wide effective format with the digital back.