[Wombat]

I cheerfully confess I'm hopeless at maths, but didn't think I was this hopeless. Here's the problem:
I have a K35/3.5 and I'm thinking of treating myself to a 77Ltd. So the difference between 35mm and 77mm is 42mm. If I want to know how this is going to look on my K7 I multiply both lenses by the crop factor of 1.5, arriving at 52.5 and 115.5 respectively. In my fuzzy brain logic tells me the difference between the two should still be 42mm, (all I've done is multiply both by the same amount), but in fact it's 63mm, a gain of 21mm in reach. Huh? And I find, furthermore, that as I double, triple etc. the length of lenses, there's an exponential increase in the differences. So, for example, from 35 to 175 is 140. Multiply both by 1.5 and you have 52.5 to 265.5, a difference of 210mm!
Would someone please tell me, slo-o-o-o-wly, what's happening here.

[moray-eel-bite]

Multiply the difference in mm by the crop factor (1.5) and I think you'll find your answer.

Cheers.

[Chaos_Realm]

Your maths Is right!
For every mm increase on a Full frame you will get 1.5mm on aps-c (if you remember back to high school) you would be familiar with a function of a straight line y=mx+c for this case:
Y= APS-C Focal Length
m=gradient of the line (Rise/Run) (1.5mm/1mm)
x=Full Frame Focal Length
c= 0 for this as a 0mm FF is the same as a 0mm APS-C

eg APS-C (Y) = FF (X) Multiplied by Crop factor (m)
75mm APS-c = 50mm on full frame X 1.5 crop

As a picture is worth a thousand words I think this is a good explanation

File:LensCropFactor.png - Wikipedia, the free encyclopedia

[Wombat]

I've carefully read your responses, guys, and thank you, but I still don't get it. In the case of the 35mm to 175mm, for example, how can you get an apparent increased reach of 210mm from a 175mm lens? And why do the differences increase exponentially when I'm simply multiplying by the same amount every time? It's not just an academic question. I'm trying to work out exactly what I can expect if I get this lens. Yes, I can play around with my 70-300 zoom, setting it on 77mm, but I like to understand as well as just see, if you get my meaning.

[Adam]

Completed disregard crop factors when it comes to FOV comparisons. Just divide the focal lengths by each other to compute the gain (or loss). 77/35 = 2.2, so your subject will be roughly twice as big through the 77mm as on the 35mm. Doesn't matter what camera you're using.

[AOShep]

Remember, you are not adding but mulitplying. To illistrate in a simpler example: if you say multiply 5 by 2 (5 x 2) you get 10. and 6 x 2 is 12. The first example you increased by 5 while the second you increased by 6 and the net gain of using 6 instead of 5 is 2.
So if is start off with a longer focal lenght lens and multiply by the crop factor or add a teleconverter the longer lens will have a proportionally greater magnification.

[Chaos_Realm]

Not sure if you saw this but its from the lens crop factor wiki and i think it visually demonstrates what your question is asking.
Below is an example at let say 75mm focal length and the dodgy modified version is say a 135mm. and if you were to continue this to further focal lengths the field of view will continue getting smaller. I hope this clears my previous explanation up a little bit for you.

EDIT: The Tree image on the sensor should be enlarged I forgot to modify that in the image :/

Attached Images

 

[Wombat]

Aaahhh, all is clear! The second round of explanations clicked in my dull, perseverating neurons. Thank you, Brothers; you've all gone to a great deal of trouble and I am humbly grateful.

[sterretje]

I'm wondering why you care? You have the 35. Going to 77mm will make your subjects 2.2 times (77 divided by 35) as big. Isn't that the only thing you actually want to know?

And it does not matter if you do these maths on APSc, film or whatever.


PS assuming infinity focused subjects

[Wombat]

I'm wondering why you care? You have the 35. Going to 77mm will make your subjects 2.2 times (77 divided by 35) as big. Isn't that the only thing you actually want to know?

I care because I like to know. I was puzzled and fascinated at the way the figures started tumbling out of control and, not being any good at maths, I wanted someone to explain it all to me so that I had a more complete understanding of where I was going. I've got lots of prime lenses and I've never really taken much notice of the maths behind the differences in focal lengths. Thanks to these guys I now know a bit more, which adds to my enjoyment of photography.

[sterretje]

It was not meant as a negative; possibly should have phrased it different.

I also like to know and understand things and will probably never stop learning things.

If I want to know how this is going to look on my K7

And that was what the rest of my answer referred to (2.2 times bigger).

[bdery]

Multiply 1 by two and then multiply 5 by two. Do you expect to get a difference of 4 or of 8?

The same applies here. Your difference would remain the same if you ADDED something, but if you multiply then your difference will be multiplied too.

Hummm.

[RioRico]

In the case of the 35mm to 175mm, for example, how can you get an apparent increased reach of 210mm from a 175mm lens?

That's just it -- you DON'T get an increased reach. You just get an image with the edges chopped off. Forget about crap.factor! It's bogus, a marketing term. Just learn what each focal length means ON YOUR CAMERA! Not on some 135/FF camera you don't have! The "apparent reach" is just image cropping, nothing more.

Your calculations are confusing because 1) if you're not a long-time 35mm (135/FF) photographer, you don't have the FOV's of various FL's imprinted in your brain, and 2) they're unnecessary. Sure, if you multiply two numbers by the same factor, their difference will multiply by the same factor too. That's trivial algebra. Look at the table Adam posted above. It tells you all you need to know about what a lens sees.

[Wombat]

Your calculations are confusing because 1) if you're not a long-time 35mm (135/FF) photographer, you don't have the FOV's of various FL's imprinted in your brain,

That's probably where the problem started, mate. I've been taking photos since I was a little tacker, 60-odd years ago, and I still have an awful lot of learning to do in the digital realm. Being weak at maths (no algebra is "trivial" to me) caused a great confusion of the brain when I started looking into this issue. But it's been hugely interesting and I'm really glad there are still hills to climb for me in photgraphy.
Sterretje, no offence taken. Bdery, thanks for your input. I've got it now.
Cheers everyone.